+127 1! + 2! + 3! ... + 100! divided by 18 has a remainder of what?
+1252 \(3*6=18\), 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
+1252 \(3*6=18\), 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
