If 100 ! = 100 x 99 x 98 x … x 2 x 1, the maximum power of 20 which will divide 100 ! is
1] 21 2] 22 3] 23 4] 24

• 20 can be written as 2^2 * 5. In 100! we have several even factors. Therefore we need not check for 2. no of factors of 5 will determine the divisibility. there are 20 multiples of 5. plus 4 factors of 25(100, 75, 50, 25). Each of them giving one extra multiple of 5. Therefore total of 24 factors of 5.
  
  therefor 100! is divisible by 20^24.
  
  hence (d).
• 12 years agoHelpfull: Yes(3) No(0)