• Take the number that you've been given the factorial of.
• Divide by 5; if you get a decimal, truncate to a whole number.
• Divide by 52 = 25; if you get a decimal, truncate to a whole number.
• Divide by 53 = 125; if you get a decimal, truncate to a whole number.
• Continue with ever-higher powers of 5, until your division results in a number less than 1. Once the division is less than 1, stop.
• Sum all the whole numbers you got in your divisions. This is the number of trailing zeroes.

Here's how the process works:

I'll apply the procedure from above:

• How many trailing zeroes would be found in 4617!, upon expansion?

  Then 4617! has 923 + 184 + 36 + 7 + 1 = 1151 trailing zeroes.

  • 51 :  4617 ÷ 5 = 923.4, so I get 923 factors of 5
  • 52 :  4617 ÷ 25 = 184.68, so I get 184 additional factors of 5
  • 53 :  4617 ÷ 125 = 36.936, so I get 36 additional factors of 5
  • 54 :  4617 ÷ 625 = 7.3872, so I get 7 additional factors of 5
  • 55 :  4617 ÷ 3125 = 1.47744, so I get 1 more factor of 5
  • 56 :  4617 ÷ 15625 = 0.295488, which is less than 1, so I stop here.

                  Then 4617! has 923 + 184 + 36 + 7 + 1 = 1151 trailing zeroes.