Question

divide 3816 by the smallest number so that the quotient is a perfect cube​

Answer 1

Prime factorising 18522, we get,

18522=2×3×3×3×7×7×7

           =21×33×73.

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

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

So we need to divide 2 from the factorization to make 18522 a perfect cube.

Hence, the smallest number by which 18522must be divided to obtain a perfect cube is 2.