MathematicsWhat is the smallest number by which 18522 must be divided so that the quotient will is a perfect cube?

What is the smallest number by which 18522 must be divided so that the quotient will is a perfect cube?

A
2
B
4
C
6
D
18

Solution:

Prime factorisation of 18522:
18522 =

2 \times 3 \times 3 \times 3 \times 7 \times 7 \times 7

To make the number a perfect cube, there should be a group of three numbers
Clearly, in the factors of 18522, 3 and 7 occur in a group of three numbers but 2 occurs only once.
Thus, the given number should be divided by 2 to make it a perfect cube.
Hence, 1 is the correct option.

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