3
Question
Find the smallest number by which 704 must be divided to obtain a perfect cube.
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Solution
By resolving 704 into prime factor,
704 = 2×2×2×2×2×2×11
By grouping the factors in triplets of equal factors,
704 = (2×2×2)×(2×2×2)×11
Here, 11 cannot be grouped into triplets of equal factors.
∴ We will divide 704 by 11 to get perfect cube.
704 = 2×2×2×2×2×2×11
By grouping the factors in triplets of equal factors,
704 = (2×2×2)×(2×2×2)×11
Here, 11 cannot be grouped into triplets of equal factors.
∴ We will divide 704 by 11 to get perfect cube.
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