If 30! × 30!/30^n is an integer, what is the largest possible value of n? Choose the correct choice from the following: A) 20 B) 14 C) 8 D) 4 E) 1
30! × 30!/30^n is an integer.   Or 30! × 30!/(3^2n*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 30! = [30/5] + [30/25] = 7   Since there are 2 20!'s, power of 7 in the numerator = 2*7= 
<gadget id="calculator">2*7</gadget>
<output>14</output>
14   Hence the largest value of b for which 30! × 30!/30^n is integer= 14   Correct Option : 14
<result>B</result>
If 30! × 30!/30^n is an integer, what is the largest possible value of n?