Modulo Calculator | 4-in-1 Modular Arithmetic Tool

Four Modular Calculators in One Tool

Explore modular arithmetic with these interactive calculators. Each demonstrates a key property of modulo operations.

1. Basic Remainder

2. Sum Modulo

3. Product Modulo

4. Power Modulo

1. Basic Remainder Calculator

Find the remainder when one number is divided by another: a mod n = r

Enter Numbers

Dividend (a)

Divisor (n) (≠ 0)

Remainder

Quotient

a mod n = ?

Step-by-Step Explanation

1 Enter numbers above and click "Calculate Remainder"

2 The remainder is what's left after division

Modular Arithmetic Properties in Action

2. Modulo of a Sum

(a + b) mod n = [(a mod n) + (b mod n)] mod n

n (modulus)

Click to calculate

3. Modulo of a Product

(a × b) mod n = [(a mod n) × (b mod n)] mod n

n (modulus)

Click to calculate

4. Modulo of a Power

a^b mod n = (a mod n)^b mod n

a (base)

b (exponent)

n (modulus)

Click to calculate

Why These Properties Matter
These three properties form the foundation of modular arithmetic. They allow us to simplify enormous calculations — for example, finding the last digit of 7^1000 or performing RSA encryption — by reducing numbers before computing powers or products.