SAGAR SINGH - IIT DELHI
Last Activity: 13 Years ago
Dear rahul,
100! = 1 x 2 x 3 x ... x 9 x 10 x ... x 15 x 20 x .... 90 x ... x 95 ... x 100
Now each of 10, 20, 30 ie.e every multiple of ten will add one zero, and hundred will add one extra. Hence total zeros = 11 (10 multiples and one extra for 100)
Now each pair of 2,5 ... 12,15... and so on will give one zero. there are 10 such pairs. So Ten more zeroes. But 75 x 72 = 5400 gives two zeroes, hence total zeroes from ths step is also 11.
now we have to account for those products groups which still leave a number 5 in tens place, this is because we have several numbers (10 total) ending in 4 which multiplied with these can give more zeroes. Remember we have already counted the 2's and the 5's in units place.
25 x 22 = 550, which multiplied by any number with 4 in units place will give one more zero
50 , which multiplied by any number with 4 in units place will give one more zero
this means two more zeroes.
Hence total number of zeroes = 11 + 11 + 2 = 24
Please feel free to ask your queries here. We are all IITians and here to help you in your IIT JEE preparation.
All the best.
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Sagar Singh
B.Tech, IIT Delhi