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How many zeros are there at the end of the number which is the product of first hundred positive integers?

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Lyndon chose this as one of his favourite problems. It is accessible but needs some careful analysis of what is included and what is not. A systematic approach is really helpful.

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Factorised Factorial

Weekly Problem 17 - 2010
The value of the factorial $n!$ is written in a different way. Can you work what $n$ must be?

N000ughty Thoughts

Age 14 to 16 Challenge Level:

Is it now well-known that factorial one hundred (written 100!) has 24 noughts when written in full and that 1000! has 249 noughts?

Convince yourself that the above is true. Perhaps your methodology will help you find the number of noughts in
10 000! and 100 000! or even 1 000 000!