Question

Find the smallest positive integer with which one has to divide 336 to get a perfect square.

Answer 1

We observe that $336=2\times 2\times 2\times 2\times 3\times 7$. Here both 3 and 7 occur only once. Hence we have to remove them to get a perfect square.
We divide 336 by 3 $\times$ 7 = 21 and get
$\frac{336}{21}=16=4^2$
The least number required is 21.