find the least number by which 392 must be multiplied so that the product becomes a perfect cube
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We will first find the prime factors of 392
392 = 2×2×2×7×7
For a number to be a perfect cube, all its prime factors must be in sets of triplets.
For 392, the 2s are in triplets, but 7 isn't.
So 392 will be multiplied by 7 to form a perfect cube, which will be 2744. Its the cube of 14.
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Here's your answer...
We will first find the prime factors of 392
392 = 2×2×2×7×7
For a number to be a perfect cube, all its prime factors must be in sets of triplets.
For 392, the 2s are in triplets, but 7 isn't.
So 392 will be multiplied by 7 to form a perfect cube, which will be 2744. Its the cube of 14.
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Answer:
Hence, 7 is the smallest number by which 392 must be multiplied so that the product is a perfect cube.
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