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Question

Divide 259875 by the smallest number so that quotient is a perfect square.

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Solution

Prime factorising, 259875=(3×3×3)×(5×5×5)×7×11.

We know, a perfect cube has multiples of 3 as powers of prime factors.

Here, the prime factor 7 and 11 does not appear in triplet form.

Therefore, 259875 is not a perfect cube.


Since in the factorization, 7 and 11 appears only one time, we must divide the number 259875 by 7×11=77, then the quotient is a perfect cube.

259875÷77=3375

=15×15×15=153, which is a perfect cube.


The smallest number by which 259875 should be divided to make it a perfect cube is 77.


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