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