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# help, and no calculators -_-

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1! + 2! + 3! ... + 100! divided by 18 has a remainder of what?

Nov 21, 2018

#1
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$$3*6=18$$, this is the integer pair of 18 where the two numbers are the closest possible. Therefore, any factorial number that is 6 or up ($$6!, 8!, 992!$$) will be divisible by 18 and have a remainder of 0.

We can do $$1!+2!+3!+4!+5!$$ which is $$1+2+6+24+120$$which equals $$153$$ .

Hopefully you know $$18\times 8=144$$ and $$153-144=9$$ So the remainder is 9.

You are very welcome!

:P

Nov 21, 2018

#1
-1

$$3*6=18$$, this is the integer pair of 18 where the two numbers are the closest possible. Therefore, any factorial number that is 6 or up ($$6!, 8!, 992!$$) will be divisible by 18 and have a remainder of 0.

We can do $$1!+2!+3!+4!+5!$$ which is $$1+2+6+24+120$$which equals $$153$$ .

Hopefully you know $$18\times 8=144$$ and $$153-144=9$$ So the remainder is 9.

You are very welcome!

:P

CoolStuffYT Nov 21, 2018
#2
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Great thinking, CS....!!!

I didn't see how to solve this, but your approach is EXACTLY what is needed...!!!   CPhill  Nov 21, 2018
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