find the natural number by which 392 must be multiplied so that the product is a perfect cube
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392=2×2×2×7×7
The prime factor 7 does not appear in a group of three. Therefore, 392 is not a perfect cube.
Now, to make its a cube, we need one more 7. 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.
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