Question

There are 36 girls and 40 boys at a summer camp. The campers will be divided into equal-sized groups. Each group will have the same number of girls and the same number of boys. What is the greatest number of groups that can be formed?

Answer 1

The maximum number groups would be 4, which contain 9 girls and 10 boys in each group.
Hope it helps.

Answer 2

The question asks you to split these numbers into smaller ones. 
This is called the prime factorization of a number: 
Lets do this for 36 first, can it be diveded by the smallest prime? (2) Yes, 36/2=18 can 18 still be dived by 2? Yes, 18/2=9 . Can 9 be divided by 2? No, so we move up in primes. Can it be divieded by 3, yes 9/3=3 and 3 is a prime so we can stop. 
What we concluded is that 36=2*2*3*3
Lets do this with 40 too, 40/2=20,  20/2=10, 10/2=5 and that is a prime so we can stop. 
40=2*2*2*5

Now will you figure out how does this help you?