Basic Examples (9) 

Find the number of factorials in the ceiling of ⅇ to the 100:

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This number is too large to compute the factorial for exactly:

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We effectively found the number of trailing zeroes in the number ⌈ⅇ¹⁰⁰⌉! =26881171418161354484126255515800135873611119!.

When I was a student at the West Virginia 2018 State Math Field Day in 10th Grade at Marshall University there was a problem my team for Huntington High School had to solve together to find I think the number of zeroes in 2018! Find the answer:

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Calculate the number of trailing zeroes of 10! in base 12:

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Find the number of trailing zeros of 100! in base 45:

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Find the number of trailing zeros in the base-17 representation of 2017!:

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Find the number of trailing zeros in the base-18 representation of 2018!:

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Find the smallest integer N such that when N! is written in base 12, it has 121 trailing zeros. Enter your answer in base 6:

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Let 3^a be the highest power of 3 that divides 1000!. What is a? Source: Floor and Ceiling Functions: Level 2 Challenges Question 5

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