number theory - Computing $bmod$s with large exponents by paper and pencil using Fermat's Little Theorem.

I'm having a bit of trouble computing $\bmod{mod}$s of large numbers using Fermat's Little Theorem.

For example, how would you compute $7^{435627650}\mod 13$? The solution given is

$435627650\mod 12=2,$ so $7^2\mod{13} = 10.$

In general, how does one solve this type of question with large exponents and mods by paper and pencil? I'm also a bit confused about where the $12$ came from and how this problem was solved.