Question

Find the smallest integer n such that 504n is a perfect square. I know it's fourteen, but could anyone please tell me a solution besides trial and error?

Answer 1

I would find the prime factorization of 504 and take the odd men out.
504 = 7*3*3*2*2*2
3*3 and 2*2 are perfect squares, 2*7 remains.

Answer 2

okay so first we need to find prime factors of 504.

2^3 * 3^2 * 7=504

separate the square terms

2^2 * 3*2 *2*7

the left out are a 2 and 7

so answer is 2*7=14