"Wiki of the Day" - Trailing zeroes question
Number Theory
Level
3
Find the trailing number of zeros in in base 21 (here 2021 is represented in base 10).
The answer is 334.
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1 solution
21 = 7 × 3
Since 7 is the bigger prime factor, it will have to be used in the calculations of trailing zeros.
Number of trailing zeros in (2021!)_21
= floor[ 2021 / 7¹ ] + floor[ 2021 / 7² ] + floor[ 2021 / 7³ ]
= 288 + 41 + 5
= 334