Question

A natural number $N$ when divided by $12$ leaves a remainder of $7$. Find the remainder when $N$ is divided by $6$.

Answer 1

Given the natural number $N$ when divided by $12$ leaves a remainder of $7$.

Let $q$ be the quotient in that case.

Then the number is $N=12q+7=12q+6+1=6(2q+1)+1\dots \left(1\right)$

Now when the number $N$ is divided by $6$ it's going to leave the reminder $1$ which is clear from $\left(1\right)$, as $6(2q+1)$ is exactly divisible by $6$.