Greatest common factor (GCF) of a set of numbers is the biggest factor that all the numbers share. X 50 = 10 5. The prime factorization of 60 is 2 x 3 x 5. 88NO. In general, they can be both positive and negative, e.g. Often in math problems, it can be desirable to find the greatest common factor of some given numbers. For most cases they are just subtraction, multiplication, or division. 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. We found the factors and prime factorization of 76 and 84. Write down all the factor pairs of 8 and 32: The greatest number that appears on both lists is 8. The three terms are: 4xy, 8xy, and xyz^5. Heres how to find the GCF:

\n

\n

1. Decompose the numbers into their prime factors.

   \n
\n

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

   \n
\n

3. Multiply the underlined numbers to get the GCF.

   \n
\n

\n

Sample questions

\n

\n

1. Find the greatest common factor of 12 and 20.

   \n

   4. Write down all the factor pairs of 12 and 20:

   \n

   Factor pairs of 12: 1 x 12, 2 x 6, 3 x 4

   \n

   Factor pairs of 20: 1 x 20, 2 x 10, 4 x 5

   \n

   The number 4 is the greatest number that appears in both lists of factor pairs, so its the GCF.

   \n
\n

2. Find the greatest common factor of 24, 36, and 42.

   \n

   6. Decompose all three numbers down to their prime factors:

   \n

   24 = 2 x 2 x 2 x 3

   \n

   36 = 2 x 2 x 3 x 3

   \n

   42 = 2 x 3 x 7

   \n

   Underline all factors that are common to all three numbers:

   \n

   24 = 2 x 2 x 2 x 3

   \n

   36 = 2 x 2 x 3 x 3

   \n

   42 = 2 x 3 x 7

   \n

   Multiply those underlined numbers to get your answer:

   \n

   2 x 3 = 6

   \n
\n

\n

Practice questions

\n

\n

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

   \n
\n

2. Whats the GCF of 8 and 32?

   \n
\n

3. Find the GCF of 30 and 45.

   \n
\n

4. Figure out the GCF of 27 and 72.

   \n
\n

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

   \n
\n

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

   \n
\n

\n

Following are the answers to the practice questions:

\n

\n

1. The GCF of 10 and 22 is 2.

   \n

   Write down all the factor pairs of 10 and 22:

   \n

   10: 1 x 10, 2 x 5

   \n

   22: 1 x 22, 2 x 11

   \n

   The number 2 is the greatest number that appears on both lists.

   \n
\n

2. The GCF of 8 and 32 is 8.

   \n

   Write down all the factor pairs of 8 and 32:

   \n

   8: 1 x 8, 2 x 4

   \n

   32: 1 x 32, 2 x 16, 4 x 8

   \n

   The greatest number that appears on both lists is 8.

   \n
\n

3. The GCF of 30 and 45 is 15.

   \n

   Write down all the factor pairs of 30 and 45:

   \n

   30: 1 x 30, 2 x 15, 3 x 10, 5 x 6

   \n

   45: 1 x 45, 3 x 15, 5 x 9

   \n

   The greatest number that appears on both lists is 15.

   \n
\n

4. The GCF of 27 and 72 is 9.

   \n

   Decompose 27 and 72 into their prime factors and underline every factor thats common to both:

   \n

   27 = 3 x 3 x 3

   \n

   72 = 2 x 2 x 2 x 3 x 3

   \n

   Multiply those underlined numbers to get your answer: 3 x 3 = 9.

   \n
\n

5. The GCF of 15, 20, and 35 is 5.

   \n

   Decompose the three numbers into their prime factors and underline every factor thats common to all three:

   \n

   15 = 3 x 5

   \n

   20 = 2 x 2 x 5

   \n

   35 = 5 x 7

   \n

   The only factor common to all three numbers is 5.

   \n
\n

6. The GCF of 44, 56, and 72 is 4.

   \n

   Decompose all three numbers to their prime factors and underline each factor thats common to all three:

   \n

   44 = 2 x 2 x 11

   \n

   56 = 2 x 2 x 2 x 7

   \n

   72 = 2 x 2 x 2 x 3 x 3

   \n

   Multiply those underlined numbers to get your answer: 2 x 2 = 4.

   \n
\n

","blurb":"","authors":[{"authorId":9399,"name":"Mark Zegarelli","slug":"mark-zegarelli","description":" Mark Zegarelli is a professional writer with degrees in both English and Math from Rutgers University. lists: It is a common factor when it is a factor of two (or more) numbers. 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. Dummies has always stood for taking on complex concepts and making them easy to understand. Using 12 as an example, in addition to 3 and 4 being factors: It can be seen that 1, 2, 3, 4, 6, and 12 are all factors of the number 12. Therefore, the common factors of 76 and 95 are 1 and 19. Factors Calculator. Let's try to solve it using Euclidean algorithm: Similarly to the previous example, the GCD of 33264 and 35640 is the last nonzero difference in the procedure, which is 2376. Now, divide 42 by 30 and get the HCF of 30 and 42 by performing the division method. lcm(a, gcf(b, c)) = gcf(lcm(a, b), lcm(a, c)). 88 = 2 2 2 11. VisualFractions.com. If you like arithmetic operations simpler than those used in the Euclidean algorithm (e.g. The factors of 12, for example, are 1, 2, 3, 4, 6 and 12. Greatest Common Factor Calculator. 2006 - 2023 CalculatorSoup To fix this, you can use prime factors. It is not difficult to see that the 'Greatest Common Factor' or 'Divisor' for 76 and 104 is 4. All Rights Reserved. Factors for 104: 1, 2, 4, 8, 13, 26, 52, and 104. The greatest common factor of 20, 50 and 120 is 10. Created by Sal Khan. The common factors between them are 1,2,4,8. The factors of 104 are 1, 2, 4, 8, 13, 26, 52 and 104. Thereafter, consider the largest common factor from the list of common factors you found as the Highest Common factor of given numbers. Otherwise, you cound find an infinite combination of distinct fractions being factors, which is pointless in our case. Level up your tech skills and stay ahead of the curve. The Euclidean algorithm uses a division algorithm combined with the observation that the GCD of two integers can also divide their difference. Factor each coefficient into primes and write the variables with exponents in expanded form. wikiHow is where trusted research and expert knowledge come together. The greatest is 4. Okay, and how to find the Greatest Common Factor of 33264 and 35640 using the binary method? That means the greatest common factor among the three terms is 1xy (or xy). If your students are beginners and have a lot to learn yet, making it easier will encourage them to keep learning more. The GCF of 15, 20, and 35 is 5. As an example: The factors of 16 include: 1, 2, 4, 8, and 16. 1. The greatest number that appears on both lists is 15. Another commonly used procedure which can be treated as a Greatest Common Divisor calculator utilizes the prime factorization. Not bad, is it? SNOW 1 THE SALEM NEWS v\l \ I HI M Snow t inches IiOW tonight 15-20. If you want to explore more about the HCF, GCF, LCM, Prime Factorization, etc. created an algorithm for finding out what the greatest common factor is in the case of two natural numbers or two polynomials? Search. "Greatest Common Factor of 76, 28, and 104". The prime factorization of 50 is 2 x 5 x 5 = 50. List of positive integer factors of 104 that divides 91 without a remainder. It can also be referred to as a common divisor. Checking shows that 3 3 7 = 63, as required. The highest number that exactly divides the given numbers with Zero Remainder is called the Highest Common Factor (HCF). You find the highest common factor by looking at which prime factors the two numbers have in common. It is also known as the Greatest Common Divisor, Greatest Common Denominator (GCD), Highest Common Factor (HCF), or Highest Common Divisor (HCD). Method 2. Find the prime factorization of 28. This can be done by hand or with the use of the LCM calculator. While estimating the Greatest Common Factor of two numbers, keep in mind these identities: As usual, let's practice the algorithm with our sets of numbers. GCF = 3 x. To find the GCF, multiply all the prime factors common to both numbers: Therefore, GCF = 2 2. because 2 6 = 12, or 4 3 = 12, or 1 12 = 12. Use HCF and LCM finder to calculate the LCM/HCF. 76 1, 2, 4, 19, 38, 76. Since you're on this page I'd guess so! If you want to make your calculation of the Highest common factor effortlessly & quickly then using the HCF Calculator is the best option. Prime factorization is only efficient for smaller integer values. We and our partners use cookies to Store and/or access information on a device. All names are used to represent a similar method of finding the highest or greatest common factor/divisor. See the Now let's find the Repeat the process subtracting the smaller number from the result until the result is smaller than the original small number. {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/6\/6b\/Find-the-Greatest-Common-Factor-Step-1-Version-2.jpg\/v4-460px-Find-the-Greatest-Common-Factor-Step-1-Version-2.jpg","bigUrl":"\/images\/thumb\/6\/6b\/Find-the-Greatest-Common-Factor-Step-1-Version-2.jpg\/aid1798549-v4-728px-Find-the-Greatest-Common-Factor-Step-1-Version-2.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"