By which smallest number must 500 be divided so that quotient is a perfect cube?​

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1. Answer:

   2

   Step-by-step explanation:

   Prime factorising 500,we get

   500 = 5 × 5 × 5 × 2 × 3

   = 5^3 × 2 ^2

   we know that , a perfect cube has multiple of 3 AS power of prime factors.

   Here, number of 2‘s is 2 and a number of 5 ‘s is 3 . so we need to multiply another 2 to the factorization to make 500 a perfect cube.

   Hence , the smallest number by which 500 must be multiplied to obtain a perfect cube is 2

   Hope it helps you

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