Multiplicative Modular Inverse Calculator

Introduction to Multiplicative Modular Inverse Calculator

Multiplicative modular inverse calculator is an online tool that helps you to find the multiplicative inverse modulo in a few seconds. Our tool evaluates the complex calculation of finding the unknown number x to get the solution of the multiplicative inverse of a given number

Our modular multiplicative inverse calculator is beneficial for anyone who want to find the gcd value of modulo that has remainder 1. That makes it a time-consuming or lengthy process to avoid all this mess in calculation use our calculator to find the multiplicative inverse modulo solution easily.

What is a Modular Multiplicative Inverse

Multiplicative inverse modulo is defined as the number that gives the remainder 1 value when you divide a number with its modulo in set theory. It is noted that not every number has a multiplicative inverse.

Those number multiplicative inverse modulo exist who have a relative prime number. Those numbers have no relative prime number as it does not give remainder 1 is not the multiplicative inverse modulo. It is a set theory topic with different methods to solve the multiplicative inverse modulo problems

Principle of Multiplicative Inverse Modulo

The principles of multiplicative inverse modulo on which Multiplicative modular inverse calculator works and solve the tricky problems is,

$$ a \;≡\; b \;(mod\; n) $$

$$ a \times n \;≡\; 1\; mod\; m $$

$$ gcd\; (a,m) \;=\; 1 $$

Here a and n are two coprime numbers, mod m is the modulo and gcd is the greatest common denominator.

How to Find Multiplicative Inverse Modulo

Multiplicative inverse modulo problems can be determined with the Euclid algorithm method. It needs a coprime number n and v for finding the multiplicative inverse modulo problems.

Although it is a little tricky method to solve modulo problems let's make it easy for you in simple steps which are used by the multiplicative inverse modulo calculator. These steps are

Step1:

First, you check the given data from the question to find the multiplicative inverse modulo

Step2:

Second, we have to find the n number which is multiplied by the given prime number v.

Step3:

Remember if you should choose that n number that is the coprime with v.

Step4:

After finding the coprime multiplication, divide with the modulo number.

Step5:

If it gives remainder 1 after division then your n number is the multiplicative inverse of the given modulo.

Note: You do not always get a number that gives remainder 1 after division. Only the coprime number gives a multiplicative inverse if it is not the coprime number then you cannot find the modulus inverse.

What is Multiplicative Inverse of 20 with Arithmetic Modulo 73

For the calculation of the multiplicative inverse of 20 modulo 73, First, Multiplicative modular inverse calculator find a number n that is multiplied by the given number such that

$$ 20 \times n \;≡\; 1\; (mod \; 73) $$

The above principle clearly shows when you multiply by 20, and it gives a remainder of 1 when coprime is divided by 73.

As per the Extended Euclidean Algorithm method modulo multiplicative inverse calculator choose different numbers using the trial and Error Method to find the exact prime number that gives the remainder 1.

Let's start with n number,n=a,a2,a3,....

For n=4:

$$ 20 \times 4 \;≡\; (mod\; 73) $$

$$ 20 \times 4 \;≡\; -7\; (mod \; 73) $$

For n=8:

$$ 20 \times 8 \;≡\; (mod\; 73) $$

$$ 20 \times 8 \;≡\; -14\; (mod\; 73) $$

For n=9:

$$ 20 \times 9 \;≡\; (mod\; 73) $$

$$ 20 \times 9 \;≡\; -34\; (mod\; 73) $$

For n=8:

$$ 20 \times 10 \;≡\; (mod\; 73) $$

$$ 20 \times 10 \;≡\; -54\; (mod\; 73) $$

For n=11:

$$ 20 \times 11 \;≡\; (mod\; 73) $$

$$ 20 \times 11 \;≡\; 1\; (mod\; 73) $$

x=11 is the multiplicative inverse of 20 modulo 73.

What is the Multiplicative Inverse of 7 Modulo 31

For the calculation of the multiplicative inverse of 7 modulo 31, First, multiplicative inverse calculator modulo find a number n that is multiplied by the given number such that

$$ 7 \times n \;≡\; 1\; (mod\; 31) $$

The above principle clearly shows when you multiply by 7, and it gives a remainder of 1 when coprime is divided by 31.

As per the Extended Euclidean Algorithm method Multiplicative modular inverse calculator choose different numbers using the trial and Error Method to find the exact prime number that gives the remainder 1.

Let's start with n number,n=1,2,3,.....n

For n=5:

$$ 7 \times 5 \;≡\; (mod\; 31) $$

$$ 7 \times 5 \;≡\; 4\; (mod\; 31) $$

For n=6:

$$ 7\times 6 \;≡\; (mod\; 31) $$

$$ 7 \times 6 \;≡\; 11\; (mod\; 31) $$

For n=7:

$$ 7 \times 7 \;≡\; (mod\; 31) $$

$$ 7 \times 7 \;≡\; 18\; (mod\; 31) $$

For n=8:

$$ 7 \times 8 \;≡\; (mod \;31) $$

$$ 7 \times 8 \;≡\; 25\; (mod\; 31) $$

For n=9:

$$ 7 \times 9 \;≡\; (mod\; 31) $$

$$ 7 \times 9 \;≡\; 1\;(mod\; 31) $$

n=9 is the multiplicative inverse of 7 modulo 31.

It is written as

$$ 1 \;≡\; 7 \times 9\; (mod\; 31) $$

$$ 1 \;≡\; 63\; (mod\; 31) $$

What is the Multiplicative Inverse of 4 Modulo 11

For the calculation of the multiplicative inverse of 4 modulo 11, First, Multiplicative modular inverse calculator find a number n that is multiplied by the given number such that

$$ 4 \times n \;≡\; 1\; (mod\; 11) $$

The above principle clearly shows when you multiply by 4, and it gives a remainder of 1 when coprime is divided by 11.

As per the Extended Euclidean Algorithm method, modular multiplicative inverse calculator choose different numbers using the trial and Error Method to find the exact prime number that gives the remainder 1.

Let's start with n number,n=1,2,3,.....n

For n=1:

$$ 4 \times 1 \;≡\; (mod\; 11) $$

$$ 4 \times 1 \;≡\; -7\; (mod\; 11) $$

For n=2:

$$ 4 \times 2 \;≡\; (mod\;11) $$

$$ 4 \times 2 \;≡\; -3(mod\;11) $$

For n=3:

$$ 4 \times 3 \;≡\; (mod\; 11) $$

$$ 4 \times 3 \;≡\; 1 \;(mod\; 11) $$

n=3 is the multiplicative inverse of 4 modulo 11.

It is written as

$$ 1 \;≡\; 4 \times 3 \;(mod\; 11) $$

$$ 1 \;≡\; 12\; (mod\; 11) $$

How to Use the Multiplicative Modular Inverse Calculator

Multiplicative inverse modulo calculator has an easy-to-use interface so that you can use it to calculate the multiplies of numbers. You just need to add “a” and modulo number and follow some simple steps to avoid trouble during the calculation process. These steps are:

1. Enter the number value of “a” in the input box.
2. Enter the modulo number value in the second input box.
3. Review your input value before clicking the calculate button to start the calculation process.
4. Click on the “Calculate” button to get the desired result of the inverse multiplicative modulo.
5. If you want to check our modulo multiplicative inverse calculator first then you can use the load example for a better understanding
6. Recalculate button get a new page for solving more inverse modulo number values in this calculator.

Final Result of the Modular Multiplicative Inverse Calculator

Multiplicative modular inverse calculator gives you the solution to a given inverse modulo number problem when you add the input into it. It gives you soluions with a complete procedure. It may contain as:

• Result Option

You can click on the result option and it provides you with a solution for Multiplicative inverse modulo problems.

• Possible Step

When you click on the possible steps option it provides you the solution of inverse modular.

Benefits of Multiplicative Inverse Modulo Calculator

Multiplicative inverse calculator modulo gives you tons of benefits whenever you use it to calculate the given number problems to find the inverse modulo. These advantages are:

• Our tool saves your time and effort from doing complex calculations of a given number in a few seconds
• Modular multiplicative inverse calculator is a free-of-cost tool so you can use it to find the inverse modulo of numbers.
• It is a versatile tool that allows you to solve various types of modulo number to solve the inverse multiplicative number
• You can use this modulo multiplicative inverse calculator to practice to get a strong hold on Multiplicative inverse modulo concept.
• It is a reliable tool that provides you with accurate solutions every time whenever you use it to calculate a given inverse modulo problem.
• It provides a solution with a complete process in a step-by-step method so that you get more clarity.
• It is an easy-to-use tool and you do not need to make any external effort to use this Multiplicative modular inverse calculator just add the input number and get a solution.