Quotient Calculator
Calculate quotient and remainder from division with step-by-step solutions
Division Calculator
The number being divided
The number to divide by (cannot be zero)
Division Results
Please enter a non-zero divisor
Example Calculations
Perfect Division
Problem: 15 ÷ 3
Quotient: 5
Remainder: 0
Result: 15 ÷ 3 = 5 R 0
With Remainder
Problem: 17 ÷ 5
Quotient: 3
Remainder: 2
Result: 17 ÷ 5 = 3 R 2
Division Terms
Dividend
The number being divided
Divisor
The number to divide by
Quotient
The result of division
Remainder
What's left over
Quick Examples
Division Facts
Division is the inverse of multiplication
Division by zero is undefined
Quotient × Divisor + Remainder = Dividend
Remainder is always less than divisor
Understanding Division and Quotients
What is Division?
Division is the mathematical operation that determines how many times one number (the divisor) is contained in another number (the dividend). It's the inverse operation of multiplication.
Division Formula
Dividend ÷ Divisor = Quotient R Remainder
Key Properties
- •Division is not commutative: a ÷ b ≠ b ÷ a
- •Division by zero is undefined
- •Any number divided by itself equals 1
- •Any number divided by 1 equals itself
Quotient and Remainder
When we divide two integers, we get a quotient (how many times the divisor goes into the dividend) and a remainder (what's left over).
Real-World Example
Pizza Problem: You have 17 pizza slices for 4 people.
17 ÷ 4 = 4 R 1
Each person gets 4 slices, with 1 slice remaining.
Verification Method
You can always verify your division: Multiply the quotient by the divisor and add the remainder. This should equal the original dividend.
(Quotient × Divisor) + Remainder = Dividend
Division Methods
Long Division
The traditional method taught in school. Divide digit by digit from left to right.
- Divide the first digit(s)
- Multiply and subtract
- Bring down next digit
- Repeat until complete
Repeated Subtraction
Keep subtracting the divisor from the dividend until you can't subtract anymore.