Remainder Calculator
Find the remainder and quotient when dividing any two numbers. This calculator shows the complete division equation, the exact decimal result, and tells you whether the numbers divide evenly.
When you divide one number by another, the result is a quotient (the whole number of times the divisor fits) and a remainder (what is left over).
The Division Algorithm:
For any integer a (dividend) and non-zero integer b (divisor):
a = q x b + r
where q is the quotient and r is the remainder. When using truncated division, the remainder has the same sign as the dividend.
Example:
29 divided by 7: quotient = 4, remainder = 1, because 29 = 4 x 7 + 1.
Remainder vs. Modulo:
These are the same for positive numbers, but they differ for negative numbers. The remainder (truncated division) keeps the sign of the dividend, while modulo (floored division) keeps the sign of the divisor. For instance, -17 divided by 5 gives remainder -2 (truncated) but modulo 3 (floored).
Practical Uses:
- Checking if a number is even or odd (divide by 2, check the remainder)
- Converting units (how many full hours and leftover minutes)
- Distributing items evenly and finding what is left over
- Programming tasks like pagination and array cycling