Remainder Calculator
Calculate quotient and remainder for division problems with step-by-step solutions
Calculate Division Remainder
The number being divided
The number to divide by (cannot be 0)
Error: Division by zero is undefined. Please enter a non-zero divisor.
Example Calculations
Example 1: Basic Division
Problem: 346 ÷ 7
Solution: 346 ÷ 7 = 49 R 3
Check: 49 × 7 + 3 = 343 + 3 = 346 ✓
As Mixed Number: 49 3/7
Example 2: Exact Division
Problem: 144 ÷ 12
Solution: 144 ÷ 12 = 12 R 0
Check: 12 × 12 + 0 = 144 ✓
Note: 144 is divisible by 12 (remainder = 0)
Example 3: Small Dividend
Problem: 5 ÷ 8
Solution: 5 ÷ 8 = 0 R 5
Check: 0 × 8 + 5 = 5 ✓
As Fraction: 5/8
Division Terms
Dividend
The number being divided
Divisor
The number you divide by
Quotient
The result of division (whole number part)
Remainder
The amount left over after division
Remainder Shortcuts
Dividing by 10
Remainder = last digit of the number
Dividing by 9
Add all digits until single digit
Dividing by 2
Even numbers have remainder 0, odd numbers have remainder 1
Quick Tips
The remainder is always smaller than the divisor
If remainder = 0, the dividend is divisible by the divisor
Division algorithm: a = q×d + r
Remainder can be expressed as a fraction: r/d
Understanding Division with Remainders
What is a Remainder?
When you divide one number by another, you might not get a whole number result. The remainder is the amount left over after division that cannot be evenly divided by the divisor.
Division Algorithm
Dividend = Quotient × Divisor + Remainder
a = q × d + r
Where 0 ≤ r < d (remainder is non-negative and less than divisor)
Real-World Applications
- •Sharing items equally among groups
- •Time calculations (converting minutes to hours)
- •Packaging problems (items per box)
- •Calendar calculations
Example Scenario
You have 25 apples to distribute equally among 6 people. Each person gets 4 apples (quotient = 4), and you have 1 apple left over (remainder = 1).