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How many zeros are at the end of (100!)(200!)(300!) when multiplied out?

 Feb 12, 2021
 #1
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The number of 0s are the number of 10s in the factor. 

This is also the number of 2 and 5s. 

But because there are always gonna be more 2s than 5s, we just need to count the number of 5s. 

For example in 10!, there are 2 fives. One 5 from 5 and one 5 from 10.

So 10! has 2 zeros. 

 

Try counting the number of 5s.

Good luck. :)))

If you need more help, just ask.

 

=^._.^=

 Feb 12, 2021
 #2
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(100/5 + 100/25 + 200/5 + 200/25 + 200/125 +300/5 + 300/25 + 300/125)==147 zeros

 Feb 12, 2021

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