Question

What is the smallest number by which 2744 be multiplied so that the product is a perfect cube

Answer 1

Answer:

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Step-by-step explanation:

In that case 392 × 7 = 2 × 2 × 2 × 7 × 7 × 7 = 2744 which is a perfect cube. Hence the smallest natural number by which 392 should be multiplied to make a perfect cube is 7.

Answer 2

Answer:

1

Explanation:

In the prime factorisation of any number,if each factor appears three times, then, is the number a perfect cube.

$\begin{array}{r | l} 2 & 2744 \\ \cline{1-2} 2 & 1372 \\ \cline{1-2} 2 & 686 \\ \cline{1-2} 7 & 343 \\ \cline{1-2} 7 & 49 \\ \cline{1-2} 7 & 7 \\ \cline{1-2} & 1 \end{array}$

By prime factorisation,2744=2×2×2×7×7×7

Each factor appears 3 times. 2744 = 2^3 × 7^3 = (2 × 7)^3

2744 is already a perfect cube

Hence the smallest natural number by which 2744 should be multiplied  to make it a perfect cube is 1