What 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?

1. A
2
2. B
4
3. C
6
4. D
18

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### Solution:

Prime factorisation of 18522:
18522 = $2×3×3×3×7×7×7$
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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