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Math Help - Need Help With Basic Prob

  1. #1
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    Post Need Help With Basic Prob

    que1> Find Number Of Zero's In The Expansion Of 79!?

    que2>find Last Two Digit Of 95!?

    do Snd The Method Also To Solve These Prob ?
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  2. #2
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    Hello, speedtijo!

    1) Find the number of zero's in the expansion of 79!

    Consider the number: . 1\cdot2\cdot3\cdot4\cdot5\cdot6\cdots 77\cdot78\cdot79

    The question becomes: how many 5's are in the factorization?
    (Since "5 times an even number" produces a 0.)

    Every fifth number has a 5: . \left[\frac{79}{5}\right] \:=\:15
    . . There are fifteen 5's among the factors.

    But a few of them two 5's . . . these are the multiples fo 25.
    . . There are: . \left[\frac{79}{25}\right] \:=\:3 of them.
    Each of these contribute an addition 5 to the factoring.

    Hence, there are: . 15 + 3 \:=\:{\bf18} factors of 5.
    . . Each of them, paired with a factor 2, produces a 10.


    Therefore, 79! has eighteen 0's at the end.



    2) Find the last two digits of 95!
    As we have seen, 79! ends in 18 zeros.

    Multiplying by 80, 81, 82, 83, ... 95, we get even more zeros at the end.

    Obviously, the last two digits are 00.

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