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⚡ Quick answer

Use the formula R = A - B × floor(A / B) to find the remainder when dividing two integers.

Modulo Calculator

Get remainder and quotient from integer-style division.

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📖 What it is

The Modulo Calculator is a handy tool for determining the remainder and quotient from integer division. It simplifies calculations that involve finding what remains after one number is divided by another.

To use the Modulo Calculator, input two integers: the dividend and the divisor. The result will show you both the remainder and how many times the divisor fits into the dividend.

Keep in mind that the divisor cannot be zero, as this will lead to undefined behavior. The calculator is designed for integer values, so using decimals may not yield accurate results in integer division contexts.

How to use

  1. Identify the dividend (A) and the divisor (B).
  2. Divide A by B and take the floor of the result.
  3. Multiply B by the floor value.
  4. Subtract this product from A to get the remainder.
  5. The result is A mod B.

📐 Formulas

  • Remainder—R = A - B × floor(A / B)
  • Floor Quotient—Q = floor(A / B)
  • Divisibility Check—isDivisible = (R == 0) ? true : false

💡 Example

For example, when calculating 23 mod 5:

1. Divide 23 by 5, which equals 4.6.

2. The floor of 4.6 is 4, meaning the divisor fits into the dividend 4 times.

3. Multiply 5 by 4 to get 20.

4. Subtract 20 from 23 to get a remainder of 3. Thus, 23 mod 5 = 3.

Real-life examples

  • Calculating Time Remainders

    If you have 50 minutes and want to know how many 15-minute intervals fit, 50 mod 15 = 5 minutes leftover.

  • Distributing Items

    If 37 candies are shared among 6 children, 37 mod 6 = 1 candy remains.

Scenario comparison

  • A = 10, B = 3—10 mod 3 = 1, meaning after dividing 10 by 3, 1 is left.
  • A = 25, B = 4—25 mod 4 = 1, indicating 1 remains after dividing 25 by 4.
  • A = 45, B = 7—45 mod 7 = 3, as 3 is the remainder when 45 is divided by 7.

Common use cases

  • Finding remainders in programming.
  • Calculating time intervals.
  • Distributing items evenly.
  • Determining page numbers in books.
  • Scheduling events in cycles.
  • Checking divisibility of numbers.
  • Managing resources in gaming.
  • Analyzing statistical data.

How it works

Modulo calculates the leftover part after performing integer division, where the remainder is identified by the formula: R = A - B × floor(A / B). If the remainder is zero, the dividend is divisible by the divisor without any leftover.

What it checks

This tool checks how much remains after dividing one number by another.

Signals & criteria

  • Dividend
  • Divisor
  • Remainder
  • Divisibility status

Typical errors to avoid

  • Setting divisor to zero.
  • Expecting modulo to always be positive for all number systems.
  • Using decimal values in workflows that assume integers.

Decision guidance

Low: If the remainder is close to the divisor, there are limited values left over from the division.
Medium: A moderate remainder indicates that the dividend is not wholly divisible by the divisor, suggesting potential rounding in practical applications.
High: A zero remainder signifies complete divisibility, showing that the dividend is exactly divisible by the divisor.

Trust workflow

Recommended steps after getting a result:

  1. Input the dividend and divisor accurately.
  2. Ensure the divisor is not zero to avoid errors.
  3. Review the results to understand the quotient and remainder.

FAQ

FAQ

  • Is modulo the same as division?

    No, modulo returns only the remainder from division.

  • When is number divisible?

    A number is evenly divisible when modulo result is zero.

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