The greatest common factor of 36 and 60 is 12. Explain what this means.

Answer 1

It helps to know that the GCF of 36 and 60 is 12 by thinking through what Greatest Common Factor means.

First, you are looking for factors or the number combinations that multiply to be 36 and 60.

Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36

Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

Next, we want to know the Common Factors or those numbers that are in both lists. I often circle the numbers that are in both lists.

You can also find the GCF by breaking them both down into their prime factors.

36 is even, so

36/2 = 18

18/2 = 9

9/3 = 3

So the prime factors of 36 are 2*2*3 = 12

60 is also even, so start with

60/2 = 30

30/2 = 15

15/3 = 5, which is prime.

You can see that except for the 5, the common prime factors with 36 are 2*2*3 = 12

Either way you break down 36 and 60, you get 12 as the greatest common factor.

Happy Factoring!

Sue H.

Answer 2

This means that 36 and 60 can both be divided by the number 12 and be considered an "integer" (whole number, not a fraction). 36 and 60 can be divided by 2, 4, 6, and 12 and yield an integer.

For example, if I divide 36 by 12, I get the number 4 (positive integer, not a fraction). If I divide 60 by 12, I get the number 5 (also a positive integer, not a fraction). If a question is asking for the "greatest" common factor, it is asking for the biggest number that 36 and 60 can be divisible by. In this case, that number is 12.