product of first fifty natural numbers

[GmatKiss]

If P is the product of first fifty natural numbers, how many times P can be completely divided by 50?

A. 1
B. 2
C. 6
D. 10
E. 12

[Toph@GMAT_REBOOT]

50 Factors to 2*5^2.

Intuitively, we know there's going to be more 2's than 5's, so we don't need to worry about having "enough" 2's.

50/5 means we reach the 10th multiple of 5s. So we at least 10 5's.

Next look at the numbers we're multiplying 5 by. 1-10. So we'll be multiplying 5 by a multiple of 5 twice. Add 2 more 5's. Therefore we have 12 5's or 6 5^2's.

Ans: D

[shankar.ashwin]

5 | 50
5 | 10
| 2

10+2 = 12. (Factors of 5)
Therefore, 6 factors of 25. C

[saketk]

Basically, we need to find the maximum power of 5 or for that matter (5^2). Number of 2's will always be more than 5. So, ignore the 2's and find only 5.

5*15*20.... *50 = 5^12 = (5^2)^6

So the answer is 6

OPTION C

[Abhishek009]

If P is the product of first fifty natural numbers, how many times P can be completely divided by 50?

A. 1
B. 2
C. 6
D. 10
E. 12

P = 1*2*3*4.............48*49*50

Or, P = 50!


Now we find the factors of 50

50 = 5^2*2

After this I followed the method as shown by Riprop...