Question

The exponent of 12 in 100 factorial

Answer 1

100! = 1x2x3x4x .... x 99 x 100

2 is a factor of 2 4 6 8 ... 98 100..so 50 of them. 2 is an additional factor in 4 8 12. 16 20 ....96 100..so 25 of these...one more 2 is a factor from 8 16 24 ... 88 96... So 12 of them. So exponent of 2 in 100! = 50+25+12+6+3+1= 97. So exponent of 4 is 97/2= 48..

Similarly exponent of 3 in 100! =
33 + 11 + 3 + 1 = 48

Exponent of 12 = smaller of exponents of 4 and 3..
ANSWER = 48