Division with Remainder
The calculator divides whole numbers with a remainder and finds the quotient and the remainder step by step, including negative numbers.
The division with remainder calculator finds the quotient and the remainder for any whole numbers, including negative ones, and shows a step-by-step solution with a check.
What is division with remainder
To divide a number a by a number b with a remainder means to find whole numbers q (the quotient) and r (the remainder) such that
a = b · q + r, where 0 ≤ r < |b|
The remainder is never negative and is always less than the divisor. If the remainder is zero, we say that a is divisible by b.
How to divide with a remainder
- Find the largest number that is divisible by the divisor and does not exceed the dividend. That number divided by the divisor is the quotient q.
- Subtract the divisor times the quotient from the dividend to get the remainder r.
- Check: the remainder is less than the divisor, and divisor · q + r equals the dividend.
Example 1. Divide 47 by 5 with a remainder.
5 · 9 = 45 ≤ 47, but 5 · 10 = 50 > 47, so q = 9.
r = 47 − 45 = 2.
Check: 5 · 9 + 2 = 47.
Answer: 47 ÷ 5 = 9 R 2
Division with remainder for negative numbers
The remainder cannot be negative, so for a negative dividend the quotient is taken one step further from zero.
Example 2. Divide −7 by 2 with a remainder.
2 · (−4) = −8 ≤ −7, but 2 · (−3) = −6 > −7, so q = −4.
r = −7 − (−8) = 1.
Answer: −7 ÷ 2 = −4 R 1
Where division with remainder is useful
- Sharing things equally: 47 candies among 5 children gives 9 each, with 2 left over.
- Converting units: 135 minutes = 2 hours 15 minutes (135 ÷ 60 = 2 R 15).
- Finding the day of the week, checking whether a number is even, divisibility rules.
For positive numbers, the result can also be written as a mixed number: 47 / 5 = 9 2/5.