Question

FIND THE SMALLEST NUMBER BY WHICH 8788 BE DIVIDED SO THAT it is PERFECT CUBE ?

Answer 1

For a given number x we define cube

of x = x × x × x , denoted by x^3.

A given Natural number is a perfect 

Cube if it can be expressed as the

product of triplets of equal factors.

Now ,

Write given number as product of

prime .

8788 = 2 × 4394

= 2 × 2 × 2197

= 2 × 2 × 13 × 169

= 2 × 2 × 13 × 13 × 13 

= 2 × 2 × ( 13 × 13 × 13 )

Here we have only triplet of equal 

factors i.e 13

To make 8788 into perfect Cube we

have multiply with 2. 

Now ,

2 × 8788 = ( 2 × 2 × 2 ) × ( 13 × 13 × 13 )


17576 = ( 2 × 13 )^3 = ( 26 )^3 perfect 

Cube

Answer 2

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=>8788=2×2×13×13×13

=>8788=2² ×13³

=>8788=4×13³

=> 48788 =13³

Hence ,while dividing 8788 with a smallest number and we get quotient is a perfect cube is 4