100100=(102)100=10200.
Now we can check the remainder of the powers of 10 being divided by 18.
102≡10mod(18)∵102−(18∗5)=10
103≡10mod(18)∵103−(18∗55)=10
104≡10mod(18)∵104−(18∗555)=10
105≡10mod(18)∵105−(18∗5555)=10
106≡10mod(18)∵106−(18∗55555)=10
...
Therefore we can conclude that the remainder of 100100 divided by 18 is 10