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How do you find the remainder of an integer division?

Published in Mathematics 2 mins read

To find the remainder of an integer division, you perform the division and identify the leftover amount that is less than the divisor.

Here's a breakdown of how to find the remainder, along with examples:

Understanding Integer Division and Remainders

When you divide two integers, the result can be expressed as a quotient and a remainder. The quotient is the whole number result of the division, and the remainder is the amount "left over" that doesn't divide evenly.

Methods to Find the Remainder

  1. Repeated Subtraction (Conceptual): You can repeatedly subtract the divisor from the dividend until you reach a number less than the divisor. That number is the remainder.

    • Example: Dividing 24 by 7.
      • 24 - 7 = 17
      • 17 - 7 = 10
      • 10 - 7 = 3
      • Since 3 is less than 7, the remainder is 3.

  2. Using the Modulo Operator (Most Common): Most programming languages and calculators have a modulo operator (often represented by % or mod) that directly returns the remainder of a division.

    • Example: 24 % 7 = 3

  3. Division and Subtraction:

    • Divide the dividend by the divisor to get the quotient (as a whole number).

    • Multiply the quotient by the divisor.

    • Subtract the result from the dividend. The result is the remainder.

    • Example: Dividing 24 by 7.

      • 24 / 7 = 3 (quotient)
      • 3 * 7 = 21
      • 24 - 21 = 3 (remainder)

Example Table

Dividend Divisor Quotient Remainder Calculation
24 7 3 3 (24 / 7 = 3); (3 * 7 = 21); (24 - 21 = 3)
17 5 3 2 (17 / 5 = 3); (3 * 5 = 15); (17 - 15 = 2)
30 6 5 0 (30 / 6 = 5); (5 * 6 = 30); (30 - 30 = 0)
10 3 3 1 (10 / 3 = 3); (3 * 3 = 9); (10 - 9 = 1)

Key Points

  • The remainder is always a non-negative integer.
  • The remainder is always less than the divisor.
  • If the remainder is 0, the division is exact (the divisor divides evenly into the dividend).

Finding the remainder is essential in various applications, including cryptography, computer science (e.g., hash tables, circular buffers), and everyday calculations.

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