Question

find the smallest number by which 704 must be divided to obtain perfect cube

Answer 1

704 =  2× 2×2×2 ×2× 2× 11
so forming pairs of cube then 11 remains unpaired so it must be divided by 11 to make it a perfect cube.

Lets verify
704÷11 =64

64 is cube of 4

Answer 2

Answer:

11 is the smallest number by which 704 must be divided to obtain perfect cube

Step-by-step explanation:

Given : Number = 704

To Find : Find the smallest number by which 704 must be divided to obtain perfect cube

Solution:

Prime factorization of 704

2  | 704

2  | 352

2  | 176

2  | 88

2  |  44

2  |  22

11  |  11

   |  1

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

when we divide 704 by 2 we get 352 which is not a perfect cube

$\sqrt[3]{352}=7.0606$

When we divide 704 by 11 we get 64 which is perfect cube

$\sqrt[3]{64}=4$

So, 11 is the smallest number by which 704 must be divided to obtain perfect cube