🔢 Multiplicative Inverse Modulo Calculator
Find modular multiplicative inverse
How to Use This Calculator
1
Enter Number and Modulus
Input a (number) and m (modulus). They must be coprime for inverse to exist.
2
Get Inverse
Find the modular inverse such that a × inverse ≡ 1 (mod m).
Formula
a × a⁻¹ ≡ 1 (mod m)
Example: a = 3, m = 7
Find x such that 3 × x ≡ 1 (mod 7)
3 × 5 = 15 ≡ 1 (mod 7) ✓
Inverse = 5
About Multiplicative Inverse Modulo Calculator
The Multiplicative Inverse Modulo Calculator finds the modular multiplicative inverse using the Extended Euclidean Algorithm.
When to Use This Calculator
- Cryptography: RSA and modular arithmetic
- Number Theory: Modular inverses
- Education: Learn inverse modulo
Why Use Our Calculator?
- ✅ Extended Euclidean: Uses efficient algorithm
- ✅ Verification: Checks if inverse is correct
- ✅ Educational: Learn modulo operations
- ✅ Completely Free: No registration required
Frequently Asked Questions
What is modular multiplicative inverse?
The modular inverse of a modulo m is a number x where a × x ≡ 1 (mod m). Used for division in modular arithmetic.
When does it exist?
Only when a and m are coprime (GCD(a,m) = 1). Example: Inverse of 3 mod 7 exists because GCD(3,7) = 1.