Question

There are 32 boys and 36 girls in the sixth grade and each student must be assigned a homeroom. Each homeroom should have the same number of boys and the same number to girls. What is the greatest possible of sixth-grade homeroom?

Answer 1

Answer: 4 sixth-grade homerooms.

Explanation:

According to the data given, each homeroom should have the same number of boys and the same number of girls. Since there are 32 boys and 36 girls, you must find the Greatest Common Divisor between theses numbers.

The steps are:

1. Descompose 36 and 32 into their prime factors:

`32=2*2*2*2*2=2^5\\\\36=2*2*3*3=2^2*3^2`

2. Multiply the commons and non commons with the lowest exponent. In this case 2 is the only common one. So:

`GCD=2^2\\\\GCD=4`

Therefore, the greatest possible of sixth-grade homeroom is 4.