A teacher has to make groups from her class of 24 boys and 18 girls. Each group will have the same number of girls. Each group will have the same...

Hello!

Denote a number of
groups as

Because each of groups should have the same number of
boys, this number must divide the number of boys, i.e.

The same
way, because each of groups should have the same number of girls, this number must
divide the number of girls, i.e.

So, must be a divisor of both
and in other words, it must be their common divisor.

The question
is what is the greatest such number and we see it is the greatest common divisor of
and

To find it, we perform prime factorisation of and

The greatest common degree of the prime factor 2 is 1 and the greatest common
degree of 3 is also 1, so the greatest common divisor is

The
answer: the maximum number of groups is 6.