3^q is a factor of (300!/100!) where q is a positive integer. What is

Definitely a >2 min question

300!/100! = 101*102*103* . . . . . . . . *298*299*300

Multiples of 3 from 101 to 300 are
102, 105, 108 . . . . .300 (AP Series, Use last term to find number of multiples)
--> 300 = 102 + (x - 1)3
--> 198/3 = x - 1
--> x = 67

Multiples of 3^2 (9) from 101 to 300 are
108, 117, 126 . . . . . 297 (AP Series, Use last term to find number of multiples)
--> 297 = 108 + (y - 1)9
--> 189/9 = y - 1
--> y = 22

Multiples of 3^3 (27) from 101 to 300 are
108, 135, 162 . . . . . 297 (AP Series, Use last term to find number of multiples)
--> 297 = 108 + (z - 1)27
--> 189/27 = z - 1
--> z = 8

Multiples of 3^4 (81) from 101 to 300 are
162, 243 = 2

Multiples of 3^5 (243) from 101 to 300 are
243 = 1

Total factors = 67 + 22 + 8 + 2 + 1 = 100

So, 300!/100! = 3^100*k, where k is any non-multiple of 3

IMO Option C

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