Finding the remainder when a large number is divided by 13 Let a number $x = 135792468135792468$. Find the remainder when $x$ is divided by $13$.
Is it possible to use Fermat's little theorem on this? I notice that the number is also repeating after $8$. 
Would really appreciate any help, thanks!

Brute force isn't demanding so much effort, actually a handful of two-digits subtractions, using the table $13,26,39,52,65,78,91,104,117$.
$$\color{blue}{13}5792468135792468\\\color{blue}{57}92468135792468\\\color{blue}{59}2468135792468\\\color{blue}{72}468135792468\\\color{blue}{74}68135792468\\\color{blue}{96}8135792468\\\color{blue}{58}135792468\\\color{blue}{61}35792468\\\color{blue}{93}5792468\\\color{blue}{25}792468\\\color{blue}{127}92468\\\color{blue}{109}2468\\\color{blue}{52}468\\\color{blue}{46}8\\\color{blue}{78}\\\color{blue}0.$$
