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avatar+128 

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

 Nov 21, 2018

Best Answer 

 #1
avatar+996 
-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

 Nov 21, 2018
 #1
avatar+996 
-1
Best Answer

\(3*6=18\), 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
avatar+106515 
0

Great thinking, CS....!!!

 

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

 

 

cool cool cool

CPhill  Nov 21, 2018
 #3
avatar+128 
+1

thanx that's the right answer 

 Nov 21, 2018

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