Question from peter, a student:

What is the largest perfect square factor of 1512?

Peter,

I am going to change the question to

What is the largest perfect square factor of 8232?

The solution is to write 24696 in terms of its prime factors.

8232 = 2^{3} × 3 × 7^{3}

2^{2} and 7^{2} are perfect square factors of 8232 and hence so is (2 × 7)^{2} = 14^{2} = 196. No larger perfect square is a factor of 8232.

Penny