🔢 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)
Try x = 5: 3 × 5 = 15 ≡ 1 (mod 7) ✓
Inverse = 5
About Inverse Modulo Calculator
The Inverse Modulo Calculator finds the modular multiplicative inverse of a number modulo m. The inverse exists only when a and m are coprime (GCD = 1).
When to Use This Calculator
- Cryptography: RSA, modular arithmetic
- Division Modulo: Perform division in modular arithmetic
- Education: Learn modular inverses
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 inverse?
The modular inverse of a modulo m is a number x such that a × x ≡ 1 (mod m). Used for division in modular arithmetic.
When does it exist?
The inverse exists only when a and m are coprime (GCD(a, m) = 1). Example: Inverse of 3 mod 7 exists because GCD(3, 7) = 1.