Bunuel wrote:
How many factors of 6! are greater than 100?
(A) 4
(B) 5
(C) 7
(D) 10
(E) 12
A good Q and not a very easy one ...
\(6! =1*2*3*4*5*6 = 2^4*3^2*5=720\)
now the trick is NOT to try and find the ONES greater than 100 BUT the ones that are required to be multiplied by factors above 100 to get 6!the lowest factors are 1,2,3,4,5,6 which can be seen from 6! if we check 6... \(\frac{6!}{6}=2*3*4*5=120>100\)
next will be 2*4=8 and \(\frac{2*3*4*5*6}{2*4}=3*5*6=90<100\)
so our answer is 1,2,3,4,5,6 so
6 valuesRealized, missed out on 1....
The OA is 6. Edited the options. Thank you.