What is the smallest natural number by which $252$ must be divided to make it a perfect square?

What is the smallest natural number by which $252$ must be divided to make it a perfect square?
  1. $7$
  2. $4$
  3. $9$
  4. $3$

Solution

$252 = 2^{2} \times 3^{2} \times 7$. The unpaired prime is $7$, so divide by $7$ to get $36 = 6^{2}$.

Asked in: IMO

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