Anticipate factorial overflow

Question

I'm wondering how could I anticipate whether the next iteration will generate an integer overflow while calculating the factorial F or not?

Let's say that at each iteration I have an int I and the maximum value is MAX_INT.

It sounds like a homework, I know. It's not. It's just me asking myself "stupid" questions.

Addendum

I though about, given a number of BITS (the width an integer can take, in bits), I could round up the number I to the next power of two, and detect if a shift to left would exceed BITS. But how would that look like, algorithmically?

Answer 1

Alternative hint:

a * b ≤ MAX_INT 

is equivalent to

a ≤ MAX_INT / b

if b > 0.