Which is the smallest number by which 8112 must be divided to get a perfect square?​

We have to find the smallest number by which 8112 should be divided to get a perfect square. Let's prime factorize 8112 to find a number which does not exist in pair:

8112 = 2 x 2 x 2 x 2 x 3 x 13 x 13

The factor 3 does not occur in pair.

Thus, '3' is the smallest number by which 8112 should be divided to get a perfect square.

• 8112/3 = 2 x 2 x 2 x 2 x 13 x 13
• 2704 = (2 x 2 x 13)²
• 2704 = 52²

2704 is a perfect cube.

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