If $7^{13}$+1 is divisible by 6 then the remainder is—

Explanation

On dividing $7^{13}$+1, by 6 Obtained remainder, $$ \frac{7^{13}+1}{6} = \frac{(6+1)^{13}+1}{6} = \frac{(+1)^{13}+1}{6} = \frac{1+1}{6} = \frac{2}{6} $$ Thus, remainder = 2