Remainder Calculator
Divide one whole number by another and get the quotient and remainder, with the answer as a mixed number and a decimal.
Change the values and press Calculate to work out your own figures.
Enter the dividend and divisor to get the whole-number quotient and the remainder.
Show the working
- 45 ÷ 7 = 6, the whole-number part
- remainder = 45 − 7 × 6 = 3
- Check: 7 × 6 + 3 = 45
How to use it
Enter the dividend and divisor to get the whole-number quotient and the remainder.
The answer is exact: whole numbers of any size up to 30 digits are handled without rounding, and Show the working lists every step.
Key facts
dividend = divisor × quotient + remainder, 0 ≤ remainder < |divisor|
Negative numbers
With negative numbers there are two conventions. Mathematics keeps the remainder between 0 and the divisor, so -45 ÷ 7 is -7 remainder 4. Many programming languages instead round the quotient toward zero, giving -6 remainder -3. Both satisfy dividend = divisor × quotient + remainder.
Questions
What is 45 divided by 7 with a remainder?
6 remainder 3, because 7 × 6 = 42 and 45 − 42 = 3.
Is the remainder the same as modulo?
For positive numbers, yes.
Formulas
dividend = divisor × quotient + remainder, 0 ≤ remainder < |divisor|
Sources
Limitations
- Numbers have at most 30 digits; factor lists and prime factorizations are limited to 10¹².