If m is the product of all integers from 1 to 40, inclusive, what is the greatest integer p for which 10^p is a factor of m?

A. 7
B. 8
C. 9
D. 10
E. 11

What's the best way to approach this kind of problems? Even after reading the answer I still struggle to apply that logic.

Thanks

m = 1 * 2 * 3 * ... 39 * 40

we need to say how many 10's we can get out of the factorization of the above.

10
20 = 10*2
30 = 10*3
40 = 10*4

we also need to consider 5's (that we could match up with 2's to get a 10

5
15
25 ... we get two 5's here
35

there are plenty of 2's to match up 32 = 2^5, 16 = 2^4

so, we can get at total of 9 10's

p = 9

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