Question

Is 1188 a perfect cube ? if not by which smallest natural number should 1188 be divided so that the quiet and is a perfect cube

Answer 1

1188=2*2*3*3*3*11

Therefore it is clearly not a perfect cube.

Hence, it should be divided by 44 to make it a

perfect cube.

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Answer 2

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1188 = 2 × 2 × 3 × 3 × 3 × 11

The primes 2 and 11 do not appear in groups of three. So, 1188 is not a perfect cube. In the factorisation of 1188 the prime 2 appears only two times and the prime 11 appears once.

So, if we divide 1188 by 2 × 2 × 11 = 44, then the prime factorisation of the quotient will not contain 2 and 11.

Hence the smallest natural number by which 1188 should be divided to make it a perfect cube is 44.

And the resulting perfect cube is 1188 ÷ 44 = 27 (=33 ).