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# Mod Calculator

Mod Calculator calculates the mod value for the given two numbers. Mod is also known as modulus or modulo. It gives the remainder after dividing one number by another number.

## What is Mod Calculator?

Mod Calculator is an online tool that helps to calculate the remainder when we are given a dividend and a divisor by applying the mod operator. In modular arithmetic, we are only interested in determining the remainder when two numbers are divided. To use this **mod calculator**, enter the values in the given input boxes.

### Mod Calculator

## How to Use Mod Calculator?

Please follow the steps below to find the remainder using the online mod calculator:

**Step 1:**Go to Cuemath’s online mod calculator.**Step 2:**Enter the two numbers in the given input boxes of the mod calculator.**Step 3:**Click on the**"Calculate"**button to find the remainder.**Step 4:**Click on the**"Reset"**button to clear the fields and enter new values.

## How Does Mod Calculator Work?

In modular arithmetic, numbers "wrap around" after reaching a given fixed quantity and leave a remainder. This given quantity is termed the modulus. The concept of modulus or modulo is heavily used in clock arithmetic. Suppose we have a 12-hour clock. Let the current time be 10:00. After 6 hours, the clock will show 4:00 rather than 16:00. We obtain this value as a result of the modulo operation. 4 is the reminder of 16 with a modulus of 12. Let a be the dividend, b be the divisor and r be the remainder. Using the modulo operation, we can represent this expression as a mod b = r. In some cases, the mod operator is denoted by the "%" symbol. Mathematically, the formula to calculate the modulo is given below:

a mod b = Dividend (a) - [Divisor (b) × Quotient]

We first multiply the divisor with the quotient. Then we subtract this value from the dividend to get the required remainder.

## Solved Examples on Mod Calculator

**Example 1:**

Find the value of 847 mod 5 and verify it using the mod calculator

**Solution:**

Given: Dividend = 847 and divisor = 5

a mod b = Dividend (a) - [Divisor (b) × Quotient]

847 mod 5 = 847 - [5 × 169]

= 847 - 845

= 2

Therefore, 847 mod 5 = 2

**Example 2:**

Find the value of 94.3 mod 6 and verify it using the mod calculator

**Solution:**

Given: Dividend = 94.3 and divisor = 6

a mod b = Dividend (a) - [Divisor (b) × Quotient]

94.3 mod 6 = 94.3 - [6 × 15]

= 94.3 - 90

= 4.3

Therefore, 94.3 mod 6 = 4.3

Similarly, you can use the mod calculator to calculate the mod value for the following:

- 50.7 mod 3.1
- 947 mod 14

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