Question

By what least number 2704 be multiplied to obtain a number which is a perfect cube

Answer 1

Step-by-step explanation:

Prime factorising 704, we get,

704=2×2×2×2×2×2×11

=2

6 ×11

1

.

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

Here, number of 2's is 6 and number of 11's is 1.

So we need to divide 11 from the factorization to make 704 a perfect cube.

Hence, the smallest number by which 704 must be divided to obtain a perfect cube is 11.

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