AP® Computer Science A · Unit 1 · Topic 1.3
Integer Division and the Mod Operator
When both operands are integers, Java's / operator throws away any remainder instead of rounding, and % gives you back exactly that discarded remainder.
A calculator treats 7 / 2 as a single real number, 3.5. Java treats it differently when both numbers are int values: it asks how many whole times 2 fits into 7, and stops there. 2 fits into 7 three whole times, with 1 left over, so 7 / 2 is 3. The .5 isn't rounded anywhere — it's simply dropped. This is called integer division, and it only behaves this way when both operands are integers; if either one is a double, Java computes the real decimal answer instead.
The mod operator, %, is the partner that rescues what division threw away. 17 / 5 asks how many groups of 5 fit inside 17: three groups, using up 15, with 2 left over. So 17 / 5 is 3, and 17 % 5 is 2, the exact remainder. Picture a number line marked off in jumps of 5: 0, 5, 10, 15, 20. The number 17 lands between the third and fourth jump, two steps past 15. Division counts the jumps you fully completed; mod measures the leftover distance.
This pairing shows up constantly once you start manipulating numbers digit by digit. Dividing by 10 with integer division chops off the last digit of a number, while taking mod 10 reads off exactly that last digit. Together they let you peel a number apart one digit at a time, which becomes a core move in later loops and algorithms built on this unit's idea that every value and every operation has a fixed, predictable type-driven behavior.
Key terms
- integer division
- Division between two integer operands in Java that discards any remainder and keeps only the whole-number result.
- mod operator (%)
- An operator that returns the remainder left over after integer division.
- truncate
- To cut off a value's fractional part without rounding it up or down.
- operand
- A value that an operator, such as / or %, acts upon.
Watch it explained
- How it worksHow does integer division throw the remainder away instead of rounding anything?
- How it worksHow does the mod operator hand back exactly the part that division discarded?
- Worked exampleFind the value of 17 / 5 and of 17 % 5, shown as groups on a number line.
- Worked exampleTrace how 1234 % 10 and 1234 / 10 peel the digits off a number one at a time.
- Common mistakeWhy isn't 7 / 2 rounded up to 4 the way ordinary rounding would do it?
Check yourself
End of topic.