What smallest number should be added to $2401$ so that the sum is completely divisible by $14$?

First, divide $2401$ by $14$ to find the remainder:
$$2401÷14$$
$$2401=14\times 171+7$$
The remainder is $7$.To make the number completely divisible by $14$, the number to be added is:
$$\text{Divisor}-\text{Remainder}=14-7=7$$