A number theory problem by Kushagra Sahni

Number Theory Level 2

Find the number of zeroes at the end of

Product of 1, 2, 3, 4, ..................1994


The answer is 495.

Kushagra Sahni by Kushagra Sahni , 21, India

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2 solutions

Satvik Golechha
Feb 14, 2014

WRONG QUESTION !! The question should've been "number of zeroes at THE END OF" and not "no of zeroes in"

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Shall I show you the book from which this question has been copied. In fact it is an RMO problem of the year 1994.

Kushagra Sahni - 7 years, 3 months ago

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Still, Kushagra, try to understand that we are finding only the number of zeros at the end of the number. How do we know whether there are any in between or not!

Satvik Golechha - 7 years, 3 months ago

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I agreed with you earlier also

Kushagra Sahni - 7 years, 3 months ago
Arya Haldar
Aug 22, 2014

I agree with Satvik, the answer is very easy- You just need have basic concept of greatest integer. [1994/5] +[1994/25]+[1994/125]+[1994/625]=398+79+15+3=398 (ans) where:[x] denotes the greatest integer of X, The logic behind it is- number of zeros formed comprises-2* 5 Since 2 is in excess, we need not worry about it, so we find number of 5 present in the equation. Since, every square multiple of 5 such as multiple of 25,125,625 has more 5^x we add them separately. We do not take the decimal part, that's why greatest integer has been introduced. Good day!

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