What is the gcf of 12 and 72 show your work

*I stand corrected by Mathstudent55. Accidentally wrote out LCM, not GCF.

The GCF is 12 as 12 is the greatest factor of itself and 12 is a factor of 72.

First, find the prime factorization of each number.

12/2 = 6
6/2 = 3
3/3 = 1

12 = 2 * 2 * 3 = 2^2 * 3

72/2 = 36
36/2 = 18
18/2 = 9
9/3 = 3
3/3 = 1

72 = 2 * 2 * 2 * 3 * 3 = 2^3 * 3^2

The GCF of two numbers is the product of some of its prime factors.
The prime factors you choose are the common factors with the smaller exponent.

Both 12 and 72 have factor 2. There is a 2^2 and a 2^3.
Choose 2^2, since that has the smaller exponent.

Both 12 and 72 have factor 3. There is a 3 and a 3^2.
Choose 3 since that has the smaller exponent.

The factors you need are 2^2 and 3

GCF = 2^2 * 3 = 4 * 3 = 12