Perfect square, but not perfect rectangle

What is the smallest positive integer n n such that the product 468 × n 468 \times n is a perfect square?


The answer is 13.

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2 solutions

468 468 factors into 2 2 × 3 2 × 13 2^2 \times 3^2 \times 13 . So 2 2 × 3 2 × 1 3 2 = 6084 2^2 \times 3^2 \times 13^2=6084 which is 7 8 2 78^2 .

Saksham Jain
Oct 26, 2017

Factorize it then check

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