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Class 12 Tuition > Learn Class XI-XII Tuition (PUC) > Number of zeros in 100!
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Number of zeros in 100!

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24. Total 11 tens + 10 pairs + 3 pairs. . Shortcut:- there are total 24 '5's within 100 .
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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 i.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...
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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 i.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 read less
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QT & DI is now a cake walk.

24
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Entrance coaching for JEE/CET (Physics, Chemistry n Maths)

2. also try to find number of zeroes in 100^100
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Entrance coaching for JEE/CET (Physics, Chemistry n Maths)

You can use the formula n!~ ( ?2?n ) (n/e)^n to find factorials.
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sir total no of '0' should be 24 .
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