When n is divided by 5, the remainder is 1. What is the remainder when 3n is divided by 5? Can I have the explanation + solution

It's pretty obvious that the remainder is 3 but what is the math behind it

Let m be a multiple of 5.

n is one more than a multiple of 5, so n=m+1

3n=3(m+1)=3m+3

3m will always be a multiple of 5 because m is a multiple of 5, so the remainder is 3.

You can also do some modulus, but Im too lazy for dat

\(\frac{n}{5}=k+\frac{1}{5}\qquad \text{k is an integer}\\ n=5k+1\\ 3n=15k+3\\ \frac{3n}{5}=3k\quad Remainder\;3 \)