A basis for your answer

Number Theory Level 3

Find the trailing zeros of the number ( ( 10 0 3 ) ! ) ((100_3)!) when it is written in base 3.


The answer is 4.

Denton Young by Denton Young , 47, USA

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1 solution

Denton Young
Jun 14, 2015

In base 3, as with all prime bases, a zero is added to n! only when there is a zero at the end of the number.

100! = 1 * 2 * 10 * 11 * 12 * 20 * 21 * 22 * 100: there are 4 zeros ( 1 from 10, one from 20 and 2 from 100.)

3 Helpful 0 Interesting 0 Brilliant 0 Confused

Seeing your answer, I think it's better to rephrase the question to:

"Find the product of all positive integers less than or equals to 100 such that its digits only consist of the numbers 0, 1, or 2. Determine the number of trailing zeros of this number."

Pi Han Goh - 5 years, 12 months ago

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i didn't get this question how to convert a number to base 3 can anyone tell @Pi Han Goh

sakshi rathore - 5 years, 10 months ago

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Well you should use a course

Mohammad Farhat - 2 years, 9 months ago

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