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1) Find the smallest number by which 13720 must be,

I. Multiplied to make it a perfect cube.
II. Divided to make it a perfect cube.

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Solution

Dear Student,

$F a c t o r s o f 13720 = 2 \times 2 \times 2 \times 7 \times 7 \times 7 \times 5 = 2^{3} \times 7^{3} \times 5 H e n c e, t o m a k e t h e f a c t o r s i n t o a p r o d u c t o f t r i p l e s o f e q u a l f a c t o r s 13, 720 m u s t b e m u l t i p l i e d b y 5 \times 5 = 25 S o, 13720 m u s t b e m u l t i p l i e d b y 25 t o m a k e i t a p e r f e c t c u b e . (i i) I f w e d i v i d e b y 5, w e g e t t r i p l e s o f 2 a n d 7 S o, 13720 m u s t b e d i v i d e d b y 5 t o m a k e i t a p e r f e c t c u b e .$

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