Question

28 The smallest number which when
multiplied with 1,37,592 will make the
product of a perfect cube is

Answer 1

Answer:

Prime factorising 137592, we get,

137592=2×2×2×3×3×3×7×7×13

              =23×33×72×13.

We know, a perfect cube has multiples of 3 as powers of prime factors.

Here, number of 2's is 3, number of 3's is 3, number of 7's is 2 and number of 13's is 1.

So we need to multiply another 7 and 132 to the factorization to make 137592 a perfect cube.

Hence, the smallest number by which 137592 must be multiplied to obtain a perfect cube is 7×132=1183.