If 60! × 60!/60^n is an integer, what is the largest possible value of n? Pick
A) 1
B) 7
C) 14
D) 28
E) 32
60! × 60!/60^n is an integer.   Or 60! × 60!/(6^2n*5^n)   This means we need to find the power of 5 in the numerator. We can safely say that the number of powers of 5 will be lower than the number of powers of 4 in the numerator.   Largest power of 5 in 60! = [60/5] + [60/25] = 14   Since there are 2 20!'s, power of 14 in the numerator = 2*14= 
<gadget id="calculator">2*14</gadget>
<output>28</output>
28   Hence the largest value of b for which 60! × 60!/60^n is integer= 28   Correct Option : 28
<result>D</result>
If 60! × 60!/60^n is an integer, what is the largest possible value of n?