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Modulo Calculator

Modulo Calculator

Calculate modulo operations and visualize the repeating patterns.

Free modulo calculator finds remainders (a mod b) with clear formulas. Perfect for programmers, students, and math enthusiasts. Supports negative numbers and sequence visualization.

Modulo Calculator: Mathematical Tool for Remainder Operations

Description

A modulo calculator computes the remainder after division of one number by another (e.g., 10 mod 3 = 1). Essential for programming, cryptography, and cyclic calculations, it visualizes repeating patterns in modular arithmetic.

What is Modulo?

Modulo (a mod b) is the remainder when a is divided by b. Example:

  • 17 mod 5 = 2 (17 ÷ 5 = 3 with remainder 2)
  • -8 mod 3 = 1 (Mathematical definition, differs by programming language)

Key Formula

a \mod b = a - b \times \lfloor a / b \rfloor

Where:

  • ⌊ ⌋ = floor function (round down)
  • Result always in range [0, b-1]

How to Use

  1. Input Values:
    • Dividend: The number to divide (e.g., 27)
    • Divisor: The modulo value (e.g., 5)
  2. Calculate: Instantly get 27 mod 5 = 2
  3. Explore: View sequence patterns (e.g., 27, 28, 29… mod 5 → 2, 3, 4, 0, 1, 2…)

FAQs

Q: Why do some languages return negative modulo results?
A: Programming languages like C++ use truncated division, while Python uses floored division. This tool follows mathematical convention (non-negative results).

Q: Can I calculate modulo with negative numbers?
A: Yes! Example: -5 mod 3 = 1 (equivalent to -5 + 3×2 = 1).

Q: What’s the practical use of modulo?
A: Clock arithmetic (12-hour time), hashing algorithms, and even music theory (octave intervals).

Terminology

  • Dividend: The number being divided (top value)
  • Divisor/Modulus: The number dividing (bottom value)
  • Residue: The remainder result
  • Congruence: Two numbers are congruent modulo n if they have the same remainder (e.g., 14 ≡ 2 mod 3)
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