Factors of 12: 1, 2, 3, 4, 12
Factors of 24: 1, 2, 3, 4, 12, 24
The common factors of 12 and 24 are numbers 1, 2, 3, 4, and 12 but the greatest common factor (GCF) of 12 and 24 is 12.
We can use prime factorization to find the GCF of two numbers.
The GCF is the product of the common prime factors.
The GCF is the product of the common prime factors.
Prime factors of 12: 12 = 2 x 2 x 3
Prime factors of 24: 24 = 2 x 2 x 2 x 3
The common prime factors are 2, 2, and 3 thus
GCF of 12 and 24 is 2 x 2 x 3 = 12.
But a shorter way is to consider both numbers and use continuous division by primes until the quotients has no common prime factors or are relatively prime. The GCF of relatively prime numbers is 1.
Example 1: Solve for the GCF of 48 and 72
2 | 48 72
2 | 24 36
2 | 12 18
3 | 6 9
2 3
GCF = 2 x 2 x 2 x 3 = 24
You may also do it on three numbers!
Example 2: Solve for the GCF of 96, 144 and 120
2 | 96 144 120
2 | 48 72 60
2 | 24 36 30
3 | 12 18 15
4 6 5
GCF = 2 x 2 x 2 x 3 = 24
