Bunuel wrote:
If 100!/x is not an integer, which of the following could be the value of x?
A. 5^24
B. 7^16
C. 11^9
D. 13^6
E. 17^6
100!/x is not an integer, this means that x has certain factors that are not common with 100!
To find out the total powers of a number in a factorial, follow this:
[100/5] +[100/5^2] + [100/5^3] = 20 + 4 + 0, where [] = integral part.
Similarly for 7, [100/7] + [100/7^2] + [100/7^3] = 14 + 2 + 0 = 16
For 11, [100/11] + [100/11^2] = 9 + 0
For 13, [100/13] + [100/13^2] = 7 + 0
For 17, [100/17] + [100/17^2] = 5 + 0
Hence the maximum power of 17 in 100! is 5
Therefore 100!/17^6 will not be an integer.
Correct Option: E