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Prime Factorisation Method to Find a Cube

Find the smal...

Question

Find the smallest number by which the following number must be divided to obtain a perfect cube.
704

A

11

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B

12

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C

14

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D

15

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Solution

The correct option is A 11
$F a c t o r i z a t i o n o f 704$

$704 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 11$

$= 2^{6} \times 11$
$T o m a k e a p e r f e c t c u b e, w e n e e d t o h a v e m u l t i p l e s o f 3 a p o w e r s o f p r i m e f a c t o r s, i . e, w e d i v i d e t h e n u m b e r b y 11$

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