greatest common factor of 28 104 and 76

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1. Decompose the numbers into their prime factors.

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2. Underline the factors that all the original numbers have in common.

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3. Multiply the underlined numbers to get the GCF.

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Sample questions

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1. 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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2. 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

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1. Find the greatest common factor of 10 and 22.

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2. Whats the GCF of 8 and 32?

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3. Find the GCF of 30 and 45.

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4. Figure out the GCF of 27 and 72.

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5. Find the GCF of 15, 20, and 35.

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6. Figure out the GCF of 44, 56, and 72.

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Following are the answers to the practice questions:

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1. 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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2. 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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3. 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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4. 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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5. 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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6. 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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The greatest common factor (GCF) of a set of numbers is the largest number thats a factor of every number in that set. Look detailed steps of finding the HCF of Numbers using a list of factors method from the below given solved example and understand the method efficiently. Find if 4 is a factor of both 76 and 48. Did you know that the mathematician Euclid of the third century B.C.E. https://www.khanacademy.org/math/pre-algebra/pre-algebra-factors-multiples/pre-algebra-greatest-common-divisor/v/greatest-common-divisor, https://www.mathsisfun.com/numbers/factors-all-tool.html, http://mathworld.wolfram.com/PrimeNumber.html, http://www.math.com/school/subject1/lessons/S1U3L2DP.html, https://www.khanacademy.org/computing/computer-science/cryptography/modarithmetic/a/the-euclidean-algorithm, GCF (Find Greatest Common Factor). It can also be referred to as a common divisor. This calculator factors a set of positive integers to find the common factors (common divisors) of those integers. GCF by factoring, list out all of the factors of each number or find them with a Another method used to determine the GCF involves using the Euclidean algorithm. In general, they can be both positive and negative, e.g. Circle the common factors in each column. x^ {\msquare} The prime factorization of 120 is 2 x 2 x 2 x 3 x 5 = 120. Then, separate the common prime factors of each number and make a list of the common prime factors. The numbers must be separated by commas, spaces or tabs or may be entered on separate lines. Start by finding all the factors of the set you are comparing. 76 Go. Volume to (Weight) Mass Converter for Recipes, Weight (Mass) to Volume to Converter for Recipes. Looking at the occurences of common prime factors in 76, 28, and 104 we can see that the commonly occuring prime factors are 2 and 2. Status: Waiting for input. Prime Factors Calculator. GCF by prime factorization, list out all of the prime factors of each number or find them with a To learn more, like how to use prime numbers to find the greatest common factor, keep reading! Subtract the result from Step 2 from the new larger number. https://www.calculatorsoup.com/calculators/math/commonfactors.php. If your given numbers are big to solve then prime factorization is the best method compared to factoring. Solution by Factorization: The factors of 8 are: 1, 2, 4, 8. Dummies helps everyone be more knowledgeable and confident in applying what they know. 2006 - 2023 CalculatorSoup Finally, multiple these common prime factors to attain the Highest Common Factor of Given Numbers. The work below shows how you can use the . So, the Greatest Common Factor for these numbers is 4 because it divides all them without a remainder. When you get the remainder zero then that divisor i.e., 6 is the HCF of given numbers. Read on to find the answer to the question: "What is the Greatest Common Factor of given numbers? The occurrences of common prime factors of 20, 50 and 120 are 2 and 5. 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. What is the Greatest Common Factor? You have reached us maybe looking for answers to the questions like: What is the greatest common factor of 76 and 104 or what is the highest common factor (HCF) of 76 and 104? Refer to the example below. For any integer k: gcf(k*a, k*b) = k * gcf(a, b), used in binary algorithm. Another concept closely related to GCD is the Least Common Multiple. Thus, the Highest Common Factor of 40 and 60 is 20. And What level of questions should I make for a test? Knowing that, let's estimate the Greatest Common Denominator of numbers 72 and 40. As an example: The factors of 16 include: 1, 2, 4, 8, and 16. When you reach zero, go back one calculation: the GCF is the number you found just before the zero result. Following this procedure, we will finally reach 0. Let's repeat the Euclidean algorithm for our examples using modulo instead of ordinary subtraction: The Greatest Common Denominator is 8. This method is somewhat related to the one previously mentioned. The average person is never likely to use prime numbers. The factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120. As a result, the Greatest Common Divisor is the last nonzero number. If you want to make your calculation of the Highest common factor effortlessly & quickly then using the HCF Calculator is the best option. Use it to try out great new products and services nationwide without paying full pricewine, food delivery, clothing and more. The greatest common factor (GCF) of a set of numbers is the largest factor that all the numbers share. It's worth knowing how this method works, but instead, we recommend to use our GCF calculator, just to make sure that the result is correct. You can calculate HCF of given numbers easily by approaching the standard methods manually. As an example: The factors of 16 include: 1, 2, 4, 8, and 16. separated by commas or spaces. Therefore, HCF(54, 60) is 6. So, the prime factorization of 104 is, 104 = 2 2 2 13 = 2 3 13. 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. Please link to this page! SNOW 1 THE SALEM NEWS v\l \ I HI M Snow t inches IiOW tonight 15-20. They have 3 and 7 in common. Along the way, he’s also paid a few bills doing housecleaning, decorative painting, and (for ten hours) retail sales. Larger values would make the prime factorization of each and the determination of the common factors, far more tedious. Decompose 27 and 72 into their prime factors and underline every factor thats common to both: Multiply those underlined numbers to get your answer: 3 x 3 = 9. Write down all the factor pairs of 30 and 45: The greatest number that appears on both lists is 15. Using multiple properties of GCF (including Least Common Multiple, LCM). Final Step: Biggest Common Factor Number. Include the highest number of occurrences of each prime factor that is common to each original number. Just right click on the above image, choose copy link address, then past it in your HTML. Thanks to all authors for creating a page that has been read 366,496 times. Bring down the common factors. The factors of 12, for example, are 1, 2, 3, 4, 6 and 12. For example, if you take two numbers ie., 54 and 60 then the Highest Common Factor of numbers is the 6 ie., the largest integer that exactly divided the two numbers with zero remainders. The examples of coprime numbers are: 5 and 7, 35 and 48, 23156 and 44613. 1. Find the greatest common factor of 24, 36, and 42. Jump to content. Calculate Reset. Please provide integers separated by a comma "," and click the "Calculate" button to find their common factors. The greatest common factor (GCF) of a set of numbers is the largest number thats a factor of every number in that set. HCF of a set of two or more numbers and see the work using factorization. Finding the GCF is helpful when you want to reduce a fraction to its lowest terms.

You can find the GCF in two ways. You can find the GCF in two ways. Now that we are aware of numerous methods of finding the Greatest Common Divisor of two numbers, you might ask: "how to find the Greatest Common Factor of three or more numbers?". But if you need to do the factorization by hand it will be a lot of work. The Greatest Common Factor Calculator solution also works as a solution for finding: The greatest common factor (GCF or GCD or HCF) of a set of whole numbers is the largest positive integer that divides evenly into all numbers with zero remainder. In this section, we will learn about factors, common factors, and greatest common factor.Before moving to the greatest common factor, first, we will understand factor and common factor. 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. 1. This is important in certain applications of mathematics such as simplifying polynomials where often it's essential to pull out common factors. Further, find the products of the multiplicands in different orders to obtain the composite factors of the number. All rights reserved. The factors of 104 are 1, 2, 4, 8, 13, 26, 52 and 104. Click "Calculate" to see all factors of each number as well as the Greatest Common Factor - Sample Math Practice Problems . In mathematics, the greatest common factor (GCF), also known as the greatest common divisor, of two (or more) non-zero integers a and b, is the largest positive integer by which both integers can be divided. We really appreciate your support! One of these involves computing the prime factorizations of each integer, determining which factors they have in common, and multiplying these factors to find the GCD. 16 = 2 2 2 2. First, in terms of numerical coefficients, the lowest coefficient in the three terms is 1. Or we can find the prime factors and combine the common ones together: 3. Since you're on this page I'd guess so! To find the Least Common Multiple, we use much of same process we used to find the GCF. As we can see there are Prime Factors common to both numbers: 2, 2. All factors of 76 : 1, 2, 4, 19, 38, 76. For additional information see our Here is a handy little calculator you can use to find the. HCF stands for Highest Common Factor also known as GCF & GCD as well. (Include only the factors common to all three numbers.). The GCF calculator evaluates the Greatest Common Factor between two to six different numbers. 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. Step 2 - GCF is the product of the factors that are common to each of the given numbers. The algorithm is as follows: From the example above, it can be seen that GCF(268442, 178296) = 2. Otherwise, you cound find an infinite combination of distinct fractions being factors, which is pointless in our case. Factors Calculator. There are multiple ways to find the greatest common factor of given integers. The three terms are: 4xy, 8xy, and xyz^5. To calculate the prime factor, we multiply these numbers together: The final method for calculating the GCF of 76, 28, and 104 is to use Euclid's algorithm. Free online Calculator that shows all the work. Also check out the Least Common Multiple of 76 and 84. Enjoy! Each time we make a subtraction we compare two numbers, ordering them from the highest to the smallest value: In our last step, we obtain 0 from subtraction. GCF (20,10). So the greatest common factor 76 and 84 is 4. Answer: GCF = 4. for the values 8, 12, 20. Toggle sidebar Rosetta Code. Learn more Finding the greatest common factor (GCF)[1] The GCF of 21 x 3, 9 x 2 and 15 x is 3 x. As a result, the product of all shared prime numbers is the answer to our problem, and what's more important, there is always one unique way to factorize any number to prime ones. We found the factors and prime factorization of 91 and 104. Use the original small number as the new larger number. The factors of 12 include: 1, 2, 3, 4, 6, and 12. Greatest common divisor is also known as greatest common factor (gcf) and greatest common. Occasional snow Friday. https://www.calculatorsoup.com - Online Calculators. Finding the GCF is helpful when you want to reduce a fraction to its lowest terms. To find the highest common factor, multiply all of the common prime factors together. Type up to 15 numbers in the text boxes below then hit 'calculate'. The greatest number that appears on both lists is 15. In the name greatest common divisor, the adjective "greatest" may be replaced by "highest", and the word "divisor" may be replaced by "factor", so that other names include highest common factor (hcf), greatest common measure, among others. The Euclidean algorithm uses a division algorithm combined with the observation that the GCD of two integers can also divide their difference. Multiply these together to get the The prime factorization of 18 is 2 x 3 x 3 = 18. Auto Calculate. Make use of the HCF Calculator provided here and calculate the highest common factor for the given numbers. Although it's quite complicated, the overall result is about 61%. A common factor is a factor that is shared between two different numbers. He has also served two years on the Tennessee Department of Education’s Common Core Leadership Council.

Jared Myracle, Ed.D. has experience in many different facets of education, including teaching and school administration. In the second step, the divisor becomes the new dividend, now divide the dividend number by divisor. \"https://sb\" : \"http://b\") + \".scorecardresearch.com/beacon.js\";el.parentNode.insertBefore(s, el);})();\r\n","enabled":true},{"pages":["all"],"location":"footer","script":"\r\n