Answer: D
Step-by-step explanation:
100!=2*3*4*...*100
Counting which numbers are divisible by 2:
2,4,6,8,10,12,14,...,96,98,100 : 50 numbers (100/2=50)
Counting which numbers are divisible by 4=2²:
4,8,12,16,20,...96,100: 25 numbers (100/4=25)
Counting which numbers are divisible by 8=2³:
8,16,24,32,40,...,96: 12 numbers (100/8=12.5 ==> 12)
Counting which numbers are divisible by 16=2⁴:
16,32,48,...,96: 6 numbers (100/16=6.25 ==> 6)
Counting which numbers are divisible by 32=2⁵:
32,64,96 : 3 numbers(100/32=3.125 ==>3)
Counting which numbers are divisible by 64=2⁶:
64 : 1 number (100/64=1.5625 ==>1)
Sum of those numbers= 50+25+12+6+3+1=97
100! is divisible by 2⁹⁷.
Answer D
