If 50! × 50!/50^n is an integer, what is the largest possible value of n?
Choose the correct choice from the following answers:  A) 36  B) 24  C) 8  D) 4  E) 2
50! × 50!/50^n is an integer.   Or 50! × 50!/(5^2n*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 50! = [50/5] + [50/25] = 12   Since there are 2 20!'s, power of 12 in the numerator 50/5  +  50/25= 
<gadget id="calculator">50/5  +  50/25</gadget>
<output>12</output>
12   Since there are 2 20!'s, power of 12 in the numerator= 2*12= 
<gadget id="calculator">2*12</gadget>
<output>24</output>
24   Hence the largest value of b for which 50! × 50!/50^n is integer= 24   Correct Option : 24
<result>B</result>
If 50! × 50!/50^n is an integer, what is the largest possible value of n?