About Remainder Calculations

The remainder operation (often called modulo) finds what's left after dividing one number by another. This calculation is fundamental in computer science, cryptography, and number theory.

How to Use This Calculator

Enter the dividend (number to be divided) in the first field
Enter the divisor (number to divide by) in the second field
Click "Compute Remainder" to see the result
Use the common modulo buttons for quick checks with standard divisors

Examples

17 ÷ 5 = 3 remainder 2 (since 5×3 = 15, and 17-15 = 2)
Even/Odd check: Any number mod 2 returns 0 for even, 1 for odd
Cyclic patterns: Modulo 7 creates weekday-like cycles (0-6)

Modulo Operation Properties

Property	Formula	Example
Distributive	(a + b) mod m = [(a mod m) + (b mod m)] mod m	(17 + 15) mod 5 = (2 + 0) mod 5 = 2
Multiplicative	(a × b) mod m = [(a mod m) × (b mod m)] mod m	(17 × 3) mod 5 = (2 × 3) mod 5 = 1

Frequently Asked Questions

What's the difference between remainder and modulo?

For positive numbers, they're identical. For negative numbers, remainder preserves the dividend's sign while modulo always returns a non-negative result.

Can the divisor be zero?

No, division by zero is undefined. The calculator will show an error if you attempt this.

What about decimal numbers?

The calculator uses integer division. Decimal inputs are truncated to integers before calculation.

Remainder Calculator

Result

Common Modulo Operations

Menu

Remainder Calculator - Quick Mod and Remainder Finder

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