By which smallest number should 42592 be divided so that the quotient is a perfect cube?
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4 is the smallest number that 42592 should be divided with so that the quotient is a perfect cube.
Step-by-step explanation:
Given,
Number = 42592
Factorization of the number 42592:
42592 = 2 * 2 * 2 * 2 * 2 * 11 * 11 * 11
= 2^3 * 2^2 * 11^3
So,
The smallest number should 42592 be divided so that the quotient is a perfect cube = 2^2
= 2 * 2
= 4
To verify,
42592 ÷ 4
= 10648
= 22 * 22 * 22
= 22^3
Thus, 4 is the smallest number that 42592 should be divided with so that the quotient is a perfect cube.
Learn more: Perfect cube
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