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?

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

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?