Remainder Calculator
Inputs
Enter two integers to perform division and find the remainder.
What is a Remainder?
In mathematics, the remainder is the amount "left over" after preforming a division of two integers (whole numbers).
If you divide 10 by 3, you can fit three 3s into 10 (making 9), and you have 1 left over. That 1 is the remainder.
Parts of Division
- Dividend: The number being divided (e.g., 10).
- Divisor: The number you divide by (e.g., 3).
- Quotient: The whole number result (e.g., 3).
- Remainder: The part left over (e.g., 1).
Dividend = (Divisor × Quotient) + Remainder
Modulo Operation
In computer science, finding the remainder is often called the modulo operation, represented by the percent symbol (%).
For example, 10 % 3 = 1. This operation is extremely useful in programming for checking if a number is even or odd (num % 2), cycling through array indexes, and cryptography.
Real World Examples
Sharing Cookies
If you have 25 cookies and want to share them equally among 4 friends:
- 25 ÷ 4 = 6
- Each friend gets 6 cookies.
- Remainder: 1 cookie is left for you!
Time Calculation
If it is currently 10:00 AM and you want to know what time it will be in 50 hours:
- 50 ÷ 24 (hours in a day) = 2 remainder 2.
- So, 2 full days will pass, plus 2 extra hours.
- 10:00 AM + 2 hours = 12:00 PM (Noon).
Frequently Asked Questions
Can the remainder be negative?
In pure arithmetic with positive numbers, no. However, in programming (like JavaScript or Python) with negative numbers, the modulo operator can return negative results depending on the language's implementation. This calculator focuses on standard Euclidean division.
What if the divisor is larger than the dividend?
If you divide a smaller number by a larger number (e.g., 3 ÷ 5), the quotient is 0 and the remainder is the dividend itself (3).
What happens if I divide by zero?
Division by zero is undefined in mathematics. This calculator will not yield a result.