Question

Is 2704 a perfect cube? If not, by which smallest natural number should 2704 be divided so that the quotient is a perfect cube?

Answer 1

Answer:

correct answer is 52

Step-by-step explanation:

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Answer 2

Answer:

The smallest natural number should 2704 be divided to get a perfect cube = 338

Step-by-step explanation:

Required to find,

1. Whether 2704 is a cube.
2. If 2704 is not a perfect cube, then the smallest natural number should be divided to get a perfect cube

Solution

Given number is 2704

The prime factorisation of 2704 = 2 ×2×2×2×13×13

= 2³×2×13²

From the prime factorisation, we can understand that 2704 cannot be expressed as the cube of its factors.

2704 is not a perfect cube.

On dividing  2³×2×13² by 2×13², we get a perfect cube, that is  2³

Hence the smallest number to be divided to get a perfect cube = 2×13²

= 338

∴The smallest natural number should 2704 be divided to get a perfect cube = 338

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