+0

# help, and no calculators -_-

0
38
3
+128

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

MATHEXPERTISE  Nov 21, 2018

#1
+422
+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
#1
+422
+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
+92787
0

Great thinking, CS....!!!

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

CPhill  Nov 21, 2018
#3
+128
+1

thanx that's the right answer

MATHEXPERTISE  Nov 21, 2018