What is the smallest number by which 2408 should be multiplied to get a perfect cube

90601

Step-by-step explanation:

we have to find  smallest number by which 2408 should be multiplied to get a perfect cube.

First lets find prime factor of 2408 and power these prime factors have

2408 = 2*1204 = 2*2*602 = 2*2*2*301= 2*2*2*7*43

thus,

2408 = 2^3*7*31

we know that a cube is a number raised to the power three

in 2408

2 has a power of three

but 7 and 31 and there is power of one,

thus we need to make

power of 7 and 31 three by multiplying

7 with 7*7

and 31 with 31*31

thus,

2^3*7*31*7*7*31*31 is the minimum cube value for this number

2^3*7*31*7*7*31*31 = 2^3*7^3*31^3 = 2408 * 7^2*31^2 = 2408*90601

Thus, smallest number which should be multiplied with 2408 to make it a perfect cube is 90601