If 10! × 10!/10^n is an integer, what is the largest possible value of n?
Select the correct option
A) 20 B) 16 C) 8 D) 4 E) 1
10! × 10!/10^n is an integer.   Or 10! × 10!/(1^2n*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 10! = [10/5] + [10/25] = 2   Since there are 2 20!'s, power of 2 in the numerator = 2*2= 
<gadget id="calculator">2*2</gadget>
<output>4</output>
4   Hence the largest value of b for which 10! × 10!/10^n is integer= 4   Correct Option : 4
<result>D</result>
If 10! × 10!/10^n is an integer, what is the largest possible value of n?