How to find the greatest common factor of 84 and 126? What is the gcf of 84 and 126?

Problem. Find the greatest common factor of 84 and 126.

Solution.

See How to find the greatest common factor of two numbers?

The prime factorization of 84

84 = 2^{2} * 3 * 7

The prime factorization of 126

126 =

2 * 3 * 3 * 7

2 * 3 * 3 * 7

Find the common prime factors of these two numbers 84 and 126

84 –> (2, 2, 3, 7)

126 –> (2, 3, 3, 7)

126 –> (2, 3, 3, 7)

The common factors of 84 and 126 are

2, 3, 7

The product of these common prime factors is the greatest common factor of 84 and 126

2 * 3 * 7 = 42

The gcf of 84 and 126 is 42

gcf(84, 126) = 42

The problem is solved.