jmc

The only numbers that leave no remainder when divided by $5$ are those that are divisible by $5$. Starting from $1,$ every five integers is divisible by $5:5,10,15,\dots$ This continues even until the last group of five numbers $96$ through $100$ where $100$ is divisible by $5$. Therefore, since we have a whole number of groups of five and every group has exactly one element that is divisible by $5$, $1/5=\boxed{20}$ percent of the integers less than $100$ have no remainders when divided by $5$.