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Greatest Common Factor

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Greatest Common Factor

Calculate the Greatest Common Factor or GCF of 42, 70, 112 and 114

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The instructions to find the GCF of 42, 70, 112 and 114 are the next:

1. Decompose all numbers into prime factors

42	2
21	3
7	7
1

70	2
35	5
7	7
1

112	2
56	2
28	2
14	2
7	7
1

114	2
57	3
19	19
1

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

Prime factors of 42	=	2 . 3 . 7
Prime factors of 70	=	2 . 5 . 7
Prime factors of 112	=	2⁴ . 7
Prime factors of 114	=	2 . 3 . 19

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 42, 70, 112 and 114

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