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Find the number of zeroes at the end of the number 55! = 1·2·…·54·55

User Gvenzl
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2 Answers

1 vote

Answer:

13 zeros

Explanation:

12696403353658275925965100847566516959580321051449436762275840000000000000

At the end are 13 zeros

User Cstrat
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5.4k points
0 votes

Answer:

13

Explanation:

A trailing zero results from a factor of 10 in the product. Such a factor is a combination of a factor of 5 and a factor of 2. At least one factor of 2 will be contributed by each even number. At least one factor of 5 wil be contributed by each number divisible by 5.

There are many more even numbers among the numbers 1–55 than there are numbers divisible by 5, so the latter will determine the number of trailing zeros.

Each number divisible by 5 will contribute 1 factor of 5. There are 55/5 = 11 such numbers. Each number divisible by 25 will contribute an additional factor of 5. There are floor(55/25) = 2 of those. So, there are a total of 11+2 = 13 factors of 5 in the number 55!. This means there are 13 trailing zeros in the number 55!.

User Jpanganiban
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5.9k points