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How many terminal zeros are at the end of (20!)?

  • Math -

    How many numbers are divisible by 5 between 1 and 20?

  • Math -

    20,15,10, and 5 are all divisible by 5. so 4. Is that how you solve for the amount of terminal zero's?

  • Math -

    uh oh my mistake. I missed a key part of the question. the question is..... How many terminal zeros are at the end of (20!)^2?

  • Math -

    The way we can get a terminal zero in a product depends on two factors (no pun intended), 2 and 5.
    There are plenty of two's between 1 and 20, namely we get three of them in 8=2^3, and 16=2^4.
    Therefore the governing factor is the number of 5's, which when combined with 2 gives a terminal zero.
    If there are four 5's between 1 and 20, then 20! will have 4 terminal zeroes.

    As you probably figured it out, squaring doubles the number of terminal zeroes.

    So if 20! has 4, then (20!)^2 should have???

    Note: watch out if and when you come to 25!
    25=5^2, so counts as 2 factors of 5.

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    alright thankyou.

  • Math -

    You're welcome!

  • Math -

    you go to sunland don't you?

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