## Introduction to Modulo Calculator

Modulo calculator is an online tool that helps you **calculate the modulo** of the given number in vector space. Our tool evaluates the remainder when one integer is divided by another and gives the remainder value in a fraction of a second.

Mod calculator is a beneficial tool for students, experts, or researchers to find the modulo of an integer because the modulo is used in different fields like programming, cryptography, and abstract algebra and has a wide range of applications in mathematics.

## What is a Module

A module is defined as a set that **operates in addition and scalar multiplication** over a ring field. It is represented by "a mod b" or "a % b" symbol in mathematics. A modulo satisfies many properties of vector spaces, involving linear independence, basis, and dimension.

For example, if you take 17 as the dividend and 5 as the divisor, the modulo is 2, because 17 divided by 5 equals 3 with a remainder of 2.

It has many applications in various mathematics fields, including linear algebra, abstract algebra, number theory, and algebraic geometry.

To calculate the modulo, you can use a modulus calculator or employ the modulus operator in programming languages such as Python, which is represented by the "%" symbol.

## How to Calculate the Modulo

To calculate the modulo operation, we **divide one number with a divisor** and get the remainder value. Here we can see an example to understand how to calculate the modulo problems step by step: For example, Find 17 modulo 5.

**Step 1:**

First, identify the given number to get to know about dividend and divisor value. In this example 17 is dividend and 5 is divisor.

**Step 2:**

Second divide 17 by 5. Since **17 divided by 5** equals 3 with a remainder of 2, the remainder (2) is the result of the modulo operation.

So, the solution of the modulo problem is 17 mod 5=2. To perform such calculations efficiently, you can use a modular calculator.

## An Example of Modulo Problem:

An **example of a modulo problem** with a solution where all the steps are mentioned that will help you to understand the working method of modular arithmetic calculator.

### Example:

Evaluate the following:

$$ 5^{29} (mod\; 11) $$

**Solution**:

Write the exponent 29 as the sum of powers of 2,

$$ 29 \;=\; 16 + 13 \;=\; 16 + 8 + 5 $$

$$ =\; 16 + 8 + 4 + 1 $$

Express 29 in base 2,

$$ 5^{29} \;=\; 5^{16 + 8 + 4 + 1} $$

$$ =\; 5^{16} . 5^{8} . 5^{4} . 5 $$

These can be obtained by means of repeated squaring,

$$ 5^1 \;=\; 5 $$

$$ 5^2 \;=\; 5^2 $$

$$ 5^4 \;=\; (5^2)^2 $$

$$ 5^8 \;=\; (5^4)^2 $$

$$ 5^{16} \;=\; (5^8)^2 $$

Reduce each intermediate result modulo 11,

$$ 5 \;=\; 5 \;(mod\; 11) $$

$$ 5^2 \;=\; 25 \;≡\; 3 \;(mod\; 11) $$

$$ 5^4 \;≡\; 3^2 \;≡\; 9 \;=\; -2 \;(mod\; 11) $$

$$ 5^8 \;≡\; 9^2 \;≡\; (-2)^2 \;=\; 4 \;(mod\; 11) $$

$$ 5^{16} \;≡\; 4^2 \;=\; 16 \;≡\; 5 \;(mod\; 11) $$

Which follows that,

$$ 5^{29} \;=\; 5^{16} . 5^{8} . 5^{4} . 5 \;≡\; 5 . 4 . (-2) . 5 \;(mod\;11) $$

Simplify,

$$ 5^{29} \;≡\; 9 \;(mod\; 11) $$

## How to Use Mod Calculator

Modulo tool has a user-friendly design that enables you to calculate the modular of particular numbers. Before using our arithmetic modulo calculator, you must follow some simple steps, and you do not face any inconvenience during the computation. These steps are:

**Enter the dividend number**value in the input box.- Enter the divisor number value in the input box.
- Review your input number before hitting the calculate button to start the evaluation process in the modulo operator calculator.
- Click the “Calculate” button to get the result of your given integer problem for division.
- You should try out the modulo tool, first, you can use the load example so that you can be assured that it provides an accurate solution.
- Click on the “Recalculate” button to get a refresh page for more solutions for modulo questions with solution

## Final Result of Modulo Calculator

Mod calculator gives you the **solution of a given integer division** problem when you add the input into it. It provides you with solutions in a detailed procedure for finding lcm from the number value instantly. It may contain as:

**Result Option**

The result option gives you a solution for the modulo problems with a solution

**Possible Steps**

It provides you with a solution where all the evaluation processes are present in a step-by-step method for modulo problems when you click on this option.

## Benefits of Using Modulus Calculator

Modular calculator provides you with multiple benefits whenever you use it to calculate integer numbers to find the value of the divisor. These benefits are:

- Modulo calculator is a free tool so you can
**use it anytime**to find the modular question from a given number in real-time without spending anything. - It is a handy tool that allows you to get the solution for numbers to find the modulo questions.
- You can try out our modulo tool to practice new examples and get a strong hold on the modular concept
- Our modular arithmetic calculator saves the time and effort that you consume in doing complex calculations and provides division problems
- The arithmetic modulo calculator is a reliable tool that provides you with accurate solutions whenever you use it for the evaluation of integers for modulo with fewer or even no mistakes.
- It provides the solution with a complete process in a stepwise method and you get clarity on the modulor method.