How many zeros are there in 100!

We have to find out the number of zero’s in 100!

Solution

To find number of zero use the given method

  • Divide 100 by 5 and its subsequent quotients by 5 as long as the quotient is nonzero (and each time ignore any nonzero remainder).
  • The final step is add up all these nonzero quotients and that will be the number of factors of 5 in 100!.

100/5 = 20

20/5 = 4

Since 4/5 has a zero quotient, we can stop here.

We notice that 20 + 4 = 24, so there are 24 factors. So 100! ends with 24 zeros.

Answer

100! ends with 24 zeros.

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