Remainder Calculator

What Is a Remainder?

Here's an illustration of the division of a number by another.

Now, there are four terms that are often used when talking about division and its results.

Dividend — The number being divided is known as the dividend. In the example above, $\hspace{0.2em} 425 \hspace{0.2em}$ is the dividend.

Divisor — Divisor is the number by which we are doing the division. In the example above, $\hspace{0.2em} 4 \hspace{0.2em}$ is the divisor.

Quotient — Quotient refers to the number of times the divisor goes into the dividend. In the example above, the quotient is $\hspace{0.2em} 106 \hspace{0.2em}$.

Remainder — Remainder is whatever is left over of the dividend after the division. In the example above, the remainder is $\hspace{0.2em} 1 \hspace{0.2em}$.

Calculating the remainder

One way to find the remainder, obviously, is to use a calculator that has a built-in function for that — like the one we have above. But we'll look at two other ways of finding the remainder when one number is divided by another.

Long Division

As we saw earlier, in the long division process, the remainder is the number left over in the end (when we have gone through all the digits in the dividend).

Here's another example.

So, when  45259  is divided by  13, the remainder is  6.

Calculators W/o a Built-In Function for Remainders

When a calculator does not give you the remainder directly, you can use the quotient to find the remainder. Here's how.

If the quotient is a whole number, it means there is no remainder. In other words the remainder is $\hspace{0.2em} 0 \hspace{0.2em}$.

For example, if we divide $\hspace{0.2em} 12 \hspace{0.2em}$ by $\hspace{0.2em} 2 \hspace{0.2em}$ on a calculator, it would tell give us $\hspace{0.2em} 6 \hspace{0.2em}$ as the answer. So, no remainder.

If the quotient has a decimal part, you can find the remainder using the following steps.

Step 1. Take the whole number part of the quotient and multiply it with the divisor.

Step 2. Subtract the product (from step 1) and subtract it from the dividend. This is your remainder.

Solution

Let's follow the steps mentioned above.

Step 1.  The whole number part of the answer $\hspace{0.2em} (24.6) \hspace{0.2em}$ is $\hspace{0.2em} 24 \hspace{0.2em}$. multiplying it by $\hspace{0.2em} 5 \hspace{0.2em}$, the divisor, we get $\hspace{0.2em} 120 \hspace{0.2em}$.

Step 2.  Subtracting the $\hspace{0.2em} 120 \hspace{0.2em}$ from $\hspace{0.2em} 123 \hspace{0.2em}$, the dividend, gives us $\hspace{0.2em} 3 \hspace{0.2em}$. And so the remainder is $\hspace{0.2em} 3 \hspace{0.2em}$.