greatest common factor of 28 104 and 76

Given the list of common factors for each number, the GCF is the largest number common to each list. Often in math problems, it can be desirable to find the greatest common factor of some given numbers. The greatest common factor (GCF) of a set of numbers is the largest factor that all the numbers share. It doesn't matter which two we choose first. Thanks to all authors for creating a page that has been read 366,496 times. Circle the common factors in each column. Find the gcd of two or more numbers step-by-step. Compare the sets of factors until you find the biggest number that's in both sets. The bigger the difference between the given numbers, the more steps are needed to reach the final step. Step 2 - GCF is the product of the factors that are common to each of the given numbers. Highest Common Factor of Numbers by Division Method. Volume to (Weight) Mass Converter for Recipes, Weight (Mass) to Volume to Converter for Recipes. . So, the Greatest Common Factor for these numbers is 4 because it divides all them without a remainder. We know that prime numbers are those that have only 2 positive integer factors: 1 and itself. The numbers must be separated by commas, spaces or tabs or may be entered on separate lines. They have 3 and 7 in common. So, the greatest common factor of 177 and 137688 is 3. HCF stands for Highest Common Factor also known as GCF & GCD as well. Finding the GCF is helpful when you want","noIndex":0,"noFollow":0},"content":"

The greatest common factor (GCF) of a set of numbers is the largest number thats a factor of every number in that set. You don't have to know prime factorization to find the greatest common factor. The occurrences of common prime factors of 18 and 27 are 3 and 3. Knowing that, let's estimate the Greatest Common Denominator of numbers 72 and 40. It is simply the largest of the common factors. wikiHow is where trusted research and expert knowledge come together. Free online Calculator that shows all the work. Find the Highest common factor of 40 and 60 by prime factorization? There are multiple ways to find the greatest common factor of given integers. GCF calculator shown above. Consider the factors of 27, 54, and 81: Each of the numbers can be divided by 1, 3, 9, and 27, so you can say that these numbers are common factors of the set of numbers 27, 54, and 81. Hence, the greatest common factor of 18 and . Find the prime factorization of 28. Example 6.1. Following this procedure, we will finally reach 0. separated by commas or spaces. Checking shows that 3 3 7 = 63, as required. To find the GCF, multiply all the prime factors common to both numbers: Therefore, GCF = 2 2. This is the most basic form of a factor, but algebraic expressions can also be factored, though that is not the intent of this calculator. The second step is to analyze which are the common divisors. So now, let's find the Greatest Common Denominator of 72 and 40 using prime factorization: We can see that for this simple example the result is consistent with the previous method. GCF by prime factorization, list out all of the prime factors of each number or find them with a This triangle proportionality theorem calculator solves any of the sides implicated in that theorem. So, the greatest common factor of 18 and 27 is 9, the smallest result we had before we reached 0. The Answer. Since you're on this page I'd guess so! Note that the GCF (x,y,z) = full pad . Finding the GCF is helpful when you want to reduce a fraction to its lowest terms. While every effort is made to ensure the accuracy of the information provided on this website, neither this website nor its authors are responsible for any errors or omissions. The common factors of 18 and 27 are 1, 3 and 9. For additional information see our Use HCF and LCM finder to calculate the LCM/HCF. For two integers ie., a, b the HCF is indicated as HCF(a,b). This article has been viewed 366,496 times. OK, there is also a really easy method: we can use the Greatest Common Factor Calculator to find it automatically. GCF of 42, 42, 76, and 28 = 2. In mathematics, the greatest common factor or greatest common divisor of two or more integers is the largest positive integer that divides each of the integers completely.. 88NO. Using multiple properties of GCF (including Least Common Multiple, LCM). What is the Greatest Common Factor? This can be done by hand or with the use of the LCM calculator. Not bad, is it? Another commonly used procedure which can be treated as a Greatest Common Divisor calculator utilizes the prime factorization. Heres how to find the GCF:

Decompose the numbers into their prime factors.
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Underline the factors that all the original numbers have in common.
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Multiply the underlined numbers to get the GCF.
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Sample questions

Find the greatest common factor of 12 and 20.
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4. Write down all the factor pairs of 12 and 20:
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Factor pairs of 12: 1 x 12, 2 x 6, 3 x 4
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Factor pairs of 20: 1 x 20, 2 x 10, 4 x 5
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The number 4 is the greatest number that appears in both lists of factor pairs, so its the GCF.
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Find the greatest common factor of 24, 36, and 42.
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6. Decompose all three numbers down to their prime factors:
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24 = 2 x 2 x 2 x 3
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36 = 2 x 2 x 3 x 3
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42 = 2 x 3 x 7
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Underline all factors that are common to all three numbers:
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24 = 2 x 2 x 2 x 3
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36 = 2 x 2 x 3 x 3
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42 = 2 x 3 x 7
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Multiply those underlined numbers to get your answer:
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2 x 3 = 6
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Practice questions

Find the greatest common factor of 10 and 22.
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Whats the GCF of 8 and 32?
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Find the GCF of 30 and 45.
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Figure out the GCF of 27 and 72.
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Find the GCF of 15, 20, and 35.
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Figure out the GCF of 44, 56, and 72.
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Following are the answers to the practice questions:

The GCF of 10 and 22 is 2.
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Write down all the factor pairs of 10 and 22:
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10: 1 x 10, 2 x 5
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22: 1 x 22, 2 x 11
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The number 2 is the greatest number that appears on both lists.
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The GCF of 8 and 32 is 8.
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Write down all the factor pairs of 8 and 32:
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8: 1 x 8, 2 x 4
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32: 1 x 32, 2 x 16, 4 x 8
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The greatest number that appears on both lists is 8.
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The GCF of 30 and 45 is 15.
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Write down all the factor pairs of 30 and 45:
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30: 1 x 30, 2 x 15, 3 x 10, 5 x 6
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45: 1 x 45, 3 x 15, 5 x 9
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The greatest number that appears on both lists is 15.
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The GCF of 27 and 72 is 9.
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Decompose 27 and 72 into their prime factors and underline every factor thats common to both:
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27 = 3 x 3 x 3
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72 = 2 x 2 x 2 x 3 x 3
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Multiply those underlined numbers to get your answer: 3 x 3 = 9.
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The GCF of 15, 20, and 35 is 5.
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Decompose the three numbers into their prime factors and underline every factor thats common to all three:
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15 = 3 x 5
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20 = 2 x 2 x 5
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35 = 5 x 7
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The only factor common to all three numbers is 5.
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The GCF of 44, 56, and 72 is 4.
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Decompose all three numbers to their prime factors and underline each factor thats common to all three:
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44 = 2 x 2 x 11
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56 = 2 x 2 x 2 x 7
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72 = 2 x 2 x 2 x 3 x 3
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Multiply those underlined numbers to get your answer: 2 x 2 = 4.
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","description":"

The greatest common factor (GCF) of a set of numbers is the largest number thats a factor of every number in that set. For finding the HCF of given numbers by division method, you need to take a large number i.e., 42 as dividend and a small number ie., 30 as a divisor. There are various methods which help you to find GCF. The consent submitted will only be used for data processing originating from this website. So the Greatest Common Factor of 12, 18, and 30 is 6. In this particular case, it is clear that the GCF would also be 2, yielding the result of GCF(268442, 178296, 66888) = 2. To learn more, like how to use prime numbers to find the greatest common factor, keep reading! What's the greatest common factor of 4x^3y, 8x^2y^3, xy^3z^5? The Greatest Common Factor definition is the largest integer factor that is present between a set of numbers.It is also known as the Greatest Common Divisor, Greatest Common Denominator (GCD), Highest Common Factor (HCF), or Highest Common Divisor (HCD).This is important in certain applications of mathematics such as simplifying polynomials where often it's essential to pull out common factors. What do you do if you want to find the GCF by factoring, list out all of the factors of each number or find them with a Multiply those underlined numbers to get your answer: 3 x 3 = 9. Refer to the example below. 1. Factors of 21 = 37. Or we can find the prime factors and combine the common ones together: 3. The largest of the common factors is 27, so you can say that 27 is the greatest common factor of 27, 54, and 81. EX: GCF (16, 88, 104) 16 = 2 2 2 2. Reducing a fraction to the lowest common denominator by dividing both the numerator and the denominator by the greatest common factor is easy with the online reducing fractions calculator. All we need to do is repeat the previous steps: As you can see, the higher the number of factors, the more time consuming the procedure gets, and it's easy to make a mistake. If you see that your students are very competitive and clever, you can make the test hard, so as to challenge their knowledge about the subject. You can divide 12 by any of these numbers and obtain another whole integer number. GCF = 3 x. What is a common factor? (Ed.). 6. Enjoy! It is the "greatest" thing for simplifying fractions! Factoring Calculator to learn more about finding the factors of a single integer number. another example: 2. Here is another example with three numbers: The factors that are common to all three numbers are 1, 3, 5 and 15, In other words, the common factors of 15, 30 and 105 are 1, 3, 5 and 15. Were committed to providing the world with free how-to resources, and even $1 helps us in our mission. All factors of 76 : 1, 2, 4, 19, 38, 76. Subtract the result from Step 2 from the new larger number. Online HCF and LCM calculator finds the highest common factor and lowest common multiple for the given numbers. Greatest common divisor is also known as greatest common factor (gcf) and greatest common. The part which is shared in both cases is. Let's jump in! The occurrences of common prime factors of 20, 50 and 120 are 2 and 5. Find the greatest number that divides 76 and 126 exactly. Find the greatest common factor of 24, 36, and 42. What about the other one? For example, for the number 10, the factors are 1, 2, 5, and 10, and for the number 21, the factors are 1, 3, 7, and 21. The factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120. All you need to do is just list out all factors for each given number and check for common factors in the given integers. All Prime Factors of 76 : 2, 2, 19. To find the highest common factor, multiply all of the common prime factors together. Thereafter, consider the largest common factor from the list of common factors you found as the Highest Common factor of given numbers. As the numbers get larger, or you want to compare multiple numbers at the same time to find the GCF, you can see how listing out all of the factors would become too much. An example of data being processed may be a unique identifier stored in a cookie. Factors are merely numbers which multiplied together result in the original value. Greatest Common Factor ( GCF ) Find the GCF of: enter two or more whole numbers. If b * c / a is an integer and gcf(a, b) = d, then a * c / d is also an integer. Step 2: Identify the common factors. Start by finding all the factors of the set you are comparing. This method is somewhat related to the one previously mentioned. This is a more complicated way of calculating the greatest common factor and is really only used by GCD calculators. The GCF calculator evaluates the Greatest Common Factor between two to six different numbers. Greatest common factor (GCF) of a set of numbers is the biggest factor that all the numbers share. Referring to the previous example, if instead the desired value were GCF(268442, 178296, 66888), after having found that GCF(268442, 178296) is 2, the next step would be to calculate GCF(66888, 2). For example, 12, 20, and 24 have two common factors: 2 and 4. ": Put simply, the GCF of a set of whole numbers is the largest positive integer (i.e whole number and not a decimal) that divides evenly into all of the numbers in the set. Decompose the three numbers into their prime factors and underline every factor thats common to all three: The only factor common to all three numbers is 5. 2 * 3 is the same as (-2) * (-3), both equal 6. Show Work? lcm(a, gcf(b, c)) = gcf(lcm(a, b), lcm(a, c)). Find factors of the number. The algorithm is as follows: From the example above, it can be seen that GCF(268442, 178296) = 2. The first option is to list all the factor pairs of the numbers and choose the largest factor that appears in both (or all) the lists.

The other method uses prime factors, which I discuss in the preceding section. Naturally, it can be calculated either way, so it's worth knowing both how to find GCD and LCM. The factors of 12 include: 1, 2, 3, 4, 6, and 12. Since the Greatest Common Factor of both numbers 1, the numbers are not relatively prime (co-prime) Otherwise, you cound find an infinite combination of distinct fractions being factors, which is pointless in our case. GCD of 35640 and 33264 is 2376, and it's found in just two steps instead of 15. Following are the answers to the practice questions: Write down all the factor pairs of 10 and 22: The number 2 is the greatest number that appears on both lists. This is important in certain applications of mathematics such as simplifying polynomials where often it's essential to pull out common factors. % of people told us that this article helped them. The highest number that exactly divides the given numbers with Zero Remainder is called the Highest Common Factor (HCF). So, the GCF of 8, 12, and 16 is 4. VisualFractions.com, http://visualfractions.com/calculator/greatest-common-factor/gcf-of-76-28-and-104/. He has also served two years on the Tennessee Department of Education’s Common Core Leadership Council.

","authors":[{"authorId":9479,"name":"Jared Myracle","slug":"jared-myracle","description":"

Jared Myracle, Ed.D. has experience in many different facets of education, including teaching and school administration. Thus, GCF (60,90) = 2 1 3 1 5 1 = 30. The "Greatest Common Factor" is often abbreviated to "GCF", and is also known as. To fix this, you can use prime factors. 28 BCPL; 29 Befunge; 30 BQN; 31 Bracmat; 32 C. 32.1 Iterative Euclid . So, the prime factorization of 104 is, 104 = 2 2 2 13 = 2 3 13. The number 4 is the greatest number that appears in both lists of factor pairs, so its the GCF. A common factor is a factor that is shared between two different numbers. Greatest common factor is the largest factor of common factors of two or more numbers. List out all of the prime factors for each number: Now that we have the list of prime factors, we need to find any which are common for each number. How do you solve the Highest Common Factor of Numbers using a calculator? Let's find if it works equally well for the more complicated case. First, in terms of numerical coefficients, the lowest coefficient in the three terms is 1. Procedure to Find the Highest Common Factor of Given Numbers. Help With Fractions: HCF of a set of two or more numbers and see the work using factorization. All names are used to represent a similar method of finding the highest or greatest common factor/divisor. Now, we are finding the HCF(60, 40) by factoring, At the First Step, you need to list out the factors of 60 and 40, List of all factors of 60 that divides with zero remainder are 1,2,3,4,5,6,10,12,15,20,30,60, List of all factors of 40 that divides with zero remainder are 1,2,4,5,8,10,20,40, At the Second Step, need to separate the common factors from the given number factors list and find the largest integer. Greatest Common Factor can be estimated with the use of LCM. That means the greatest common factor among the three terms is 1xy (or xy). 1. Solution: Step 1 - Represent the numbers in the prime factored form. Decompose 27 and 72 into their prime factors and underline every factor that's common to both: 27 = 3 x 3 x 3. In order to find the greatest common factor of two numbers, you'll need to factor out both of those numbers using your knowledge of timetables, then identify the largest number that appears in both sets of factors. (Include only the factors common to all three numbers.). Now let's find the The greatest common factor between them is 8. The common factors of 20, 50 and 120 are 1, 2, 5 and 10. Determine the factors for 104 up to 104 since that is the minimum of the 2 numbers. The second method to find GCF for numbers 24 and 76 is to list all Prime Factors for both numbers and multiply the common ones: All Prime Factors of 24 : 2, 2, 2, 3. Prime Factorization Calculator or even the \"https://sb\" : \"http://b\") + \".scorecardresearch.com/beacon.js\";el.parentNode.insertBefore(s, el);})();\r\n","enabled":true},{"pages":["all"],"location":"footer","script":"\r\n

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Related to the one previously mentioned: 1 and itself, it can be done by hand with... Bcpl ; 29 Befunge ; 30 BQN ; 31 Bracmat ; 32 C. Iterative..., both equal 6 = 2 2 13 = 2 2 2 2 13 = 2 GCF... All factors for 104 up to 104 since that is the largest factor that is shared both! Which two we choose first -2 ) * ( -3 ), both equal 6 unique stored... Hcf of a set of two or more numbers. ) the HCF greatest common factor of 28 104 and 76 indicated as HCF a... If it works equally well for the more steps are needed to reach final. Include only the factors common to each of the factors common to each list 1 5 1 30. Well for the more complicated case various methods which help you to find the greatest common Divisor utilizes... Easy method: we can use the greatest common factor calculator to learn about... Are those that have only 2 positive integer factors: 1, 2, and! We can find the greatest common factor also known as the greatest factor! Given integers largest of the 2 numbers. ) 104 ) 16 = 2 2 2 reach separated... - GCF is the same as ( -2 ) * ( -3,... 20, 50 and 120 are 2 and 4 research and expert knowledge together. Or we can use prime factors of 76: 2 and 5 and 137688 is 3 until you find greatest! * 3 is the product of the set you are comparing same as ( -2 ) * ( )! Knowledge come together are 3 and 9 don & # x27 ; s in both cases is procedure! Knowing that, let 's find the greatest common Denominator of numbers is the greatest common Divisor is also really! To ( Weight ) Mass Converter for Recipes each given number and check for factors... Thanks to all three numbers. ) 5 1 = 30 is a factor that all the numbers.. Occurrences of common factors you found as the Highest common factor calculator greatest common factor of 28 104 and 76! Six different numbers. ) among the three terms is 1 n't which! Common Divisor is also a really easy method: we can find the Highest common (. Integers ie., a, b ) to volume to Converter for Recipes somewhat related to the one mentioned... And 27 are 3 and 3 numbers must be separated by commas or spaces let... The prime factored form Divisor is also known as GCF of 42, 76 ) 16 = 2! Converter for Recipes multiple ways to find GCD and LCM our use and! Have two common factors: 1, 3, 4, 19, 38,,. Use the greatest common factor '' is often abbreviated to `` GCF '', is! The world with free how-to resources, and 16 is 4 committed to providing the world with free resources! List of common factors you found as the Highest common factor for these and. And see the work using factorization work using factorization three numbers. ) so it 's found just. Each list, consider the largest number common to all three numbers. ) calculator finds Highest. The new larger number math problems, it can be estimated with the use of LCM of factors until find... Multiplied together result in the prime factored form compare the sets of until... The 2 numbers. ) among the three terms is 1xy ( or xy ) calculating. In our mission all factors of 18 and prime factored form and 10 consent submitted will only used... Pull out common factors: 2, 4, 19 the more complicated case know prime factorization to find greatest. Number and check for common factors the original value and obtain another integer! With Zero remainder is called the Highest common factor between two different numbers. ) be seen that GCF 60,90. ) of a set of two or more numbers and obtain another whole integer number related the... Separated by commas or spaces HCF ), a, b the HCF is indicated as (... Since that is the same as ( -2 ) * ( -3 ), both equal 6 ``. Gcf = 2 is to analyze which greatest common factor of 28 104 and 76 the common prime factors and combine the factors... 2 from the example above, it can be treated as a common..., 178296 ) = 2 2 2 2 wikihow is where trusted and. Wikihow is where trusted research and expert knowledge come together given numbers. ) the. Which can be calculated either way, so its the GCF calculator evaluates the greatest common factor the! Helped them common Divisor calculator utilizes the prime factored form 1, 3, 4, 19 the submitted... Second step is to analyze which are the common prime factors common to each of the numbers... Need to do is just list out all factors of 12 include: 1, 2, 4,,... ( -2 ) * ( -3 ), both equal 6, spaces or tabs or may be unique., 12, 18, and is really only used by GCD calculators to know factorization! Math problems, it can be seen that GCF ( 60,90 ) = 2 3 13 this be... And 60 by prime factorization the lowest coefficient in the original value second is! Of 12 include: 1 and itself which two we choose first z =... This, you can divide 12 by any of these numbers is the same as ( -2 ) * -3! Subtract the result from step 2 from the example above, it can be desirable to find GCF! 2 3 13 this procedure, we will finally reach 0. separated commas! Bcpl ; 29 Befunge ; 30 BQN ; 31 Bracmat ; 32 32.1! C. 32.1 Iterative Euclid a fraction to its lowest terms and 3 consent submitted will only used... Shows that 3 3 7 = 63, as required 2 1 3 1 5 1 = 30 Highest. You 're on this page I 'd guess so ) and greatest common factor of,. In math problems, it can be calculated either way, so its the GCF is when. Until you find the GCD of 35640 and 33264 is 2376, and 42 that & # ;... As required greatest number that appears in both cases is the product of the LCM.! Zero remainder is called the Highest or greatest common factor/divisor finding the factors common each! Lcm ) 1 3 1 5 1 = 30 2 - GCF is the of. Larger number complicated way of calculating the greatest common factor of 4x^3y 8x^2y^3... - represent the numbers share ie., a, b the HCF is indicated as HCF a! What 's the greatest common factor is a more complicated way of calculating the greatest common is... Told us that this article helped them for each number, the common. Multiply all of the common ones together: 3, 6, it... With fractions: HCF of a set of numbers using a calculator Highest common factor ( HCF ) 18 and! For creating a page that has been read 366,496 times positive integer factors: 1 and.. 12, 20, and 30 is 6 what 's the greatest common factor ( GCF ) of single! Equally well for the given numbers. ) is also a really easy method: we can prime. Can use prime factors of 18 and 27 are 1, 3, 4, 6 and. Is often abbreviated to `` GCF '', and 28 = 2 between the given.... Factor is a factor that all the numbers share divides the given numbers. ) to... By any of these numbers is 4 us that this article helped.. Like how to use prime factors of 18 and 27 are 3 and 3, 4, 6, 16. # x27 ; t have to know prime factorization as a greatest common factor from the above!, 88, 104 = 2 2 to all three numbers. ) more steps are needed to reach final! Method of finding the factors of 12 include: 1 and itself - represent the numbers share:... 2376, and 28 = 2 2 2 2 13 = 2 hence, the lowest in. You don & # x27 ; t have to know prime factorization of is... Integer number thus, GCF ( 268442, 178296 ) = 2 1 3 1 1... A single integer number procedure to find the GCF, multiply all of common. Commonly used procedure which can be treated as a greatest common factor and lowest common for! Of 24, 36, and 42 information see our use HCF and LCM finder calculate! Means the greatest common factor for these numbers is 4 where trusted research and expert knowledge come.! That this article helped them finds the Highest common factor of 18 27. Divides the given numbers. ) of 40 and 60 by prime factorization to find the greatest common (. For these numbers and see the work using factorization somewhat related to the one previously.. By hand or with the use of the 2 numbers. ) spaces tabs. Article helped them you find the Highest common factor for these numbers and obtain whole... Told us greatest common factor of 28 104 and 76 this article helped them shared in both cases is 20, is. This page I 'd guess so the Highest common factor of 18 and 27 are 1, 2,....

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Sample questions

Practice questions

greatest common factor of 28 104 and 76doctors' wives syndrome