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| Math Central | Quandaries & Queries |
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Question from Yvonne, a parent: Hi, The numbers 756 and 72, expressed as products of prime factors, are 756 = 2² x 3³ x 7 and 72 = 2³ x 3² Use these result to find, the smallest integer, x, such that 756x is a perfect cube. Thanks you |
Hi Yvonne,
8 = 23, 27 = 33, 216 = 23 × 33 = 63, 64 = 26 = 43 are all cubes. For n to be a cube it must be that the powers of the primes in the prime factor decomposition of n must be divisible by 3.
Penny
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