Integer division, including remainders, is usually a two stage process and…

The idea

Integer division discards any fractional part and keeps only the whole-number quotient. Because a single division loses the remainder, the usual approach is two stages: first divide to get the whole-number quotient, then use modular arithmetic (the remainder operator) to recover what is left over. For example, sharing 17 items among 5 people gives a quotient of 3 each, and 17 mod 5 gives a remainder of 2. In code you might write quotient = 17 div 5 and remainder = 17 mod 5, or use your language's integer-division and remainder symbols. Always check the order: divide first, then take the remainder of the same operands.

What earns the marks

• Integer division returns only the whole-number part of a quotient, discarding any fractional remainder.
• The remainder is found using modular arithmetic, typically the mod operator, applied to the same two operands.
• The two-stage process means dividing to obtain the quotient and then separately calculating the remainder.
• Worked example: 17 divided by 5 gives an integer quotient of 3 and a remainder of 2, since 3 × 5 = 15 and 17 − 15 = 2.
• The remainder must be smaller than the divisor, which acts as a check on a correct answer.

Common mistakes and how to put them right

• Confusing integer division with real division and expecting a decimal result.

  Put it right by remembering integer division keeps only the whole-number quotient.

• Reporting the remainder as the quotient or vice versa.

  Put it right: Keep the two stages separate and label each result clearly.

• Forgetting that the remainder is always less than the divisor.

  Put it right: Use this as a quick check on any answer.

Exam tips

• Show both stages explicitly: state the whole-number quotient and then the remainder.
• Use a small worked example such as 17 and 5 to verify your method before answering.
• Check that your remainder is smaller than the divisor; if not, re-examine your division.