Question

Find the smallest positive integer, n,such that 168n is a square number.​

Answer 1

• n = 42 and the square number is 7056

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Prime factors of 168 are:

• 168 = 2*2*2*3*7

In order to make 168n a square number we need to use each prime factor even number of times.

Add 2, 3 and 7 to the prime factors (as a minimum) to get:

• 168*2*3*7 = 168*42 = 2⁴*3²*7² = (2²*3*7)² = 84² = 7056