To find a composite number why divide by prime numbers?

Answer 1

You could try dividing by composite numbers but the number that you are testing is divisible by a composite number, then it will be divisible by a prime factor of that composite number and that prime factor will be smaller. It is always easier to work with smaller numbers.

Answer 2

The very definition of "composite number" is that you can split it up into smaller factors. Eventually, you can express any number as a product of one or more prime numbers.