Question

what is the smallest no. by which 13068 should be divided,so the quotient is a perfect square?

Answer 1

Let's factorize 13068 by LCM.

2 | 13068

2 | 6534

3 | 3267

3 | 1089

3 | 363

11 | 121

11 | 11

| 1

13068 = 2² x 3³ x 11²

2² x 3³ x 11² divided by 3 gives 2² x 3² x 11² = (2 x 3 x 11)² = 66².

So 3 is the smallest number by which 13068 is divided to get a perfect square as quotient.

13068 ÷ 3 = 4356 = 66²

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