Table of Contents

- 1 Do prime numbers have multiplicative inverses?
- 2 How do you find the multiplicative inverse of a number?
- 3 What is the multiplicative inverse of minus 7 by 8?
- 4 How do you do inverse mod on a calculator?
- 5 What is the multiplicative inverse of p/q?
- 6 How do you find the multiplicative inverse of a given GCD?

## Do prime numbers have multiplicative inverses?

Thus if m is prime, the only number between 0 and m-1 that does not have a mod m multiplicative inverse is 0. For example, take m=7. The numbers from 0 to 14 that have common divisors with 15 are 0, 3, 5, 9, and 10.

## How do you find the multiplicative inverse of a number?

For the multiplicative inverse of a real number, divide 1 by the number. For example, the reciprocal of 5 is one fifth (1/5 or 0.2), and the reciprocal of 0.25 is 1 divided by 0.25, or 4.

**What is the multiplicative inverse of P ‘?**

Multiplication Inverse of Fraction If p/q is a fraction, then the multiplicative inverse of p/q should be such that, when it is multiplied to the fraction, then the result should be 1. Hence, q/p is the multiplicative inverse of fraction p/q.

### What is the multiplicative inverse of minus 7 by 8?

Multiplicative inverse of -8/7 is -7/8.

### How do you do inverse mod on a calculator?

To calculate the value of the modulo inverse, use the extended euclidean algorithm which find solutions to the Bezout identity au+bv=G.C.D. (a,b) ( a , b ) . Here, the gcd value is known, it is 1 : G.C.D.

**How to find the modular multiplicative inverse of a prime number?**

An efficient solution is based on extended Euclid algorithm. ax + by = gcd (a, b) Let us put b = prime, we get ax + prime * y = gcd (a, prime) We know gcd (a, prime) = 1 because on of the numbers is prime. So we know ax + prime * y = 1 Since prime * y is a multiple of prime, x is modular multiplicative inverse of a . ax ≡ 1 (mod prime)

#### What is the multiplicative inverse of p/q?

If p/q is a fraction, then the multiplicative inverse of p/q should be such that, when it is multiplied to the fraction, then the result should be 1. Hence, q/p is the multiplicative inverse of fraction p/q. Mul.

#### How do you find the multiplicative inverse of a given GCD?

The idea is to use Extended Euclidean algorithms that takes two integers ‘a’ and ‘b’, finds their gcd and also find ‘x’ and ‘y’ such that ax + by = gcd (a, b) To find multiplicative inverse of ‘a’ under ‘m’, we put b = m in above formula. Since we know that a and m are relatively prime, we can put value of gcd as 1.

**How to find the multiplicative inverse of mixed fraction?**

To find the multiplicative inverse of mixed fraction, firstly convert it into a proper fraction. Let us see some examples. Let us see some of the methods to the proof modular multiplicative inverse. Method 1: For the given two integers say ‘a’ and ‘m’, find the modular multiplicative inverse of ‘a’ under modulo ‘m’.