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Greatest Common Factor

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Greatest Common Factor

Calculate the Greatest Common Factor or GCF of 38, 76, 114 and 130

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The instructions to find the GCF of 38, 76, 114 and 130 are the next:

1. Decompose all numbers into prime factors

38	2
19	19
1

76	2
38	2
19	19
1

114	2
57	3
19	19
1

130	2
65	5
13	13
1

2. Write all numbers as the product of its prime factors

Prime factors of 38	=	2 . 19
Prime factors of 76	=	2² . 19
Prime factors of 114	=	2 . 3 . 19
Prime factors of 130	=	2 . 5 . 13

3. Choose the common prime factors with the lowest exponent

Common prime factors: 2

Common prime factors with the lowest exponent: 2¹

4. Calculate the Greatest Common Factor or GCF

Remember, to find the GCF of several numbers you must multiply the common prime factors with the lowest exponent.

GCF = 2¹ = 2

Also calculates the:

Least Common Multiple or LCM of 38, 76, 114 and 130

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