How-many-zeroes-0-there-in-1-2-3-4-99-100-

Question Number 20907 by DKumar last updated on 07/Sep/17

H o w m a n y z e r o e s (0) t h e r e i n 1 \times 2 \times 3 \times 4 \dots \dots \dots . 99 \times 100

Answered by dioph last updated on 07/Sep/17

zeros in number = maximum integer

n such that 10^{n} = 2^{n} 5^{n} divides the number .

As there is plenty more factors of 2 than

factors of 5, we will find n = number

of factors of 5 .

There is one for each multiple of 5

between 1 and 100 (20 of them) +

another one for each multiple of

25 between 1 and 100 (4 of them) .

Hence, 100! ends in 24 zeros .

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