AJP wrote:now i am asking this how to find cube root of 175616...........
not by prime factorization method

by a new method

It would be nice if you included the answer choices.
On the GMAT, you'd never have to actually calculate the cube root of 175,616.
Instead you could either use the answer choices to your advantage. Or you could estimate.

Here's one way to estimate.

cuberoot(175,616) is close to cuberoot(175,000)
cuberoot(175,000) = cuberoot(175 x 1000)
= cuberoot(175) x cuberoot(1000)
= cuberoot(175) x 10

Let's examine cuberoot(175)
Since cuberoot(125) = 5 and cuberoot(216) = 6, we know that cuberoot(175) = 5.something

So, we get ...
cuberoot(175 x 1000) = cuberoot(175) x cuberoot(1000)
= 5.something x 10
= fifty something.
The real value is 56

We could also have used some number sense to see that the units digit of cuberoot(175,616) must be 6 (since 6x6x6 = some value with 6 as units digit)

Cheers,
Brent