Remainder

Definition

The remainder is the amount left over after performing a division when one number does not evenly divide another. It is an integer less than the divisor in any base system.

5 Must Know Facts For Your Next Test

1. In base-10, if you divide 23 by 5, the remainder is 3.
2. The remainder can be found using the modulo operation, often represented as % in programming languages.
3. In base systems other than 10, remainders are calculated similarly but may have different digit representations.
4. When converting numbers between bases, remainders help determine each digit of the new base representation.
5. The Euclidean algorithm uses remainders to find the greatest common divisor (GCD) of two numbers.

Review Questions

• What is the remainder when 29 is divided by 4?
• How would you express finding a remainder using a modulo operation?
• Why are remainders important in base conversion?

Related terms

Divisor: The number by which another number is divided.

Modulo Operation: A mathematical operation that returns the remainder after division.

Euclidean Algorithm: An algorithm used to find the greatest common divisor of two integers through repeated division and taking remainders.