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Math Help - factorial help

  1. #1
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    factorial help

    20! has 4 zeros at its end whereas 25! has 6 zeros..

    how come..
    somebody help..
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  2. #2
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    Re: factorial help

    i dont get your question
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  3. #3
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    Re: factorial help

    Hi hitesh091,

    i'm assuming that you need to reason out only the increase in the no. of zeroes in 25! from the 4 zeroes in 20!

    in order to find the 25! you'll have to multiply 20! with 21, 22, 23, 24 and 25, right?

    consider the product 24x25 = 600, the two zeroes in this product will add to the already existing 4 zeroes of 20!. This leads to the increase of the number of zeroes from 4 to 6 when you compute 25!

    hope it helped....
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  4. #4
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    Re: factorial help

    There is nothing peculiar or special ig you observe 20! you can find that there are only 4 numbers which can give zero like, 10, 20,, 15 *4, 12*6 and similarly for 25! you can work out.
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  5. #5
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    Re: factorial help

    Quote Originally Posted by hitesh091 View Post
    20! has 4 zeros at its end whereas 25! has 6 zeros..
    how come..
    somebody help..
    Every trailing zero in n! results in the number of factors of fives in n!.

    26! is divisible by 5,~10,~15,~20,~\&~25=5^2 that is six factors of five.

    50! has 12 trailing zeros. Fifty is has 10 factors of 5 and 2 factors of 25.
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  6. #6
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    Re: factorial help

    @ max09 thanks i got it..
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