Integer Division — Definition, Formula & Examples
Integer division is division between two integers where you keep only the whole-number part of the result, discarding any fractional remainder. For example, 17 divided by 5 gives an integer quotient of 3 with a remainder of 2.
Given integers (the dividend) and (the divisor), integer division produces a unique pair of integers (quotient) and (remainder) such that , where .
Key Formula
Where:
- = The dividend (the integer being divided)
- = The divisor (the integer you divide by; cannot be 0)
- = The quotient (whole-number result of the division)
- = The remainder (what is left over)
How It Works
Start by asking how many times the divisor fits completely into the dividend. That count is the quotient. Multiply the quotient by the divisor and subtract the product from the dividend to find the remainder. The remainder is always a non-negative integer smaller than the absolute value of the divisor. If the remainder is 0, the divisor divides the dividend evenly.
Worked Example
Problem: Perform integer division: 23 ÷ 4.
Find the quotient: Determine how many times 4 fits entirely into 23.
Find the remainder: Subtract the product from the dividend.
Verify: Check that the relationship holds and the remainder is valid.
Answer: The integer quotient is 5 with a remainder of 3.
Why It Matters
Integer division appears whenever you split items into equal groups — sharing 23 stickers among 4 friends gives each person 5 with 3 left over. It also forms the basis of the division algorithm used in number theory and is essential in computer science, where most programming languages have a dedicated integer division operator.
Common Mistakes
Mistake: Reporting the quotient as a decimal (e.g., 23 ÷ 4 = 5.75) instead of separating the quotient and remainder.
Correction: In integer division, keep the quotient as a whole number and state the remainder separately: quotient 5, remainder 3.