representation of a number as multiplication of its factors
I know one...
If you're using python, you can use dictionary's to simplify the storage...
You'll have to check for every prime less than square root of the number.
Now, suppose p^k divides your number n, your task, I suppose is to find k.
Here's the method:

int c = 0; int temp = n; while(temp!=0) { temp /= p; c+= temp; }

The above is a C++ code but you'll get the idea...
At the end of this loop you'll have c = k
And yeah, the link given by will is a perfect python implementation of the same algorithm
I want to represent a number as the product of its factors.The number of factors that are used to represent the number should be from 2 to number of prime factors of the same number(this i s the maximum possible number of factors for a number).
for example taking the number 24:
representation of the number as two factors multiplication are 2*12, 8*3, 6*4 and so on...,
representation of the number as three factors multiplication are 2*2*6, 2*3*4 and so on...,
representation of the number as four factors multiplication(prime factors alone) are 2*2*2*3.
please help me get some simple and generic algorithm for this