MOD & DIV (AS Level)

• MOD and DIV are arithmetic operators for integer division.
• MOD returns the REMAINDER after division.
• DIV returns the QUOTIENT (integer part) after division.
• Both operators work with INTEGER values only.
• These are AS Level topics — not required at IGCSE, although some IGCSE questions do use MOD.

Example — 17 divided by 5:

// 17 divided by 5
17 DIV 5 = 3   // quotient: 5 goes into 17 three times (3 x 5 = 15)
17 MOD 5 = 2   // remainder: 17 - 15 = 2

DIV performs integer division — it returns the whole-number quotient and discards the decimal part (it does NOT round).

Syntax: result <- dividend DIV divisor

DECLARE Result : INTEGER
Result <- 17 DIV 5
OUTPUT Result   // Outputs: 3

More examples:

10 DIV 3  returns 3   // 10 / 3 = 3.33..., integer part = 3
20 DIV 4  returns 5   // 20 / 4 = 5 exactly
7 DIV 2   returns 3   // 7 / 2 = 3.5, integer part = 3
15 DIV 6  returns 2   // 15 / 6 = 2.5, integer part = 2

• Truncates, never rounds: 7 DIV 2 = 3 (not 4), because the .5 is discarded.
• Exact division: when there is no remainder, DIV gives the exact quotient (20 DIV 4 = 5).
• Result type: always an INTEGER — never a REAL.

MOD returns the remainder after integer division.

Syntax: result <- dividend MOD divisor

DECLARE Result : INTEGER
Result <- 17 MOD 5
OUTPUT Result   // Outputs: 2

More examples:

10 MOD 3  returns 1   // 10 = 3 x 3 + 1
20 MOD 4  returns 0   // 20 = 4 x 5 + 0, no remainder
7 MOD 2   returns 1   // 7 = 2 x 3 + 1
15 MOD 6  returns 3   // 15 = 6 x 2 + 3

• MOD 0 means exact division: 20 MOD 4 = 0 because 4 divides exactly into 20.
• Result range: X MOD Y is always in the range 0 to Y−1.
• Result type: always an INTEGER — never a REAL.

• Even / Odd check: Num MOD 2 = 0 means even; Num MOD 2 = 1 means odd.
• Extract digits: Num MOD 10 gives the last digit; Num DIV 10 removes the last digit.
• Time conversion: convert minutes into hours and remaining minutes.
• Currency / change: calculate the count of coins or bills of each denomination.
• Divisibility test: A MOD B = 0 means A is divisible by B.

Example — extract the digits of a 3-digit number:

DECLARE Num : INTEGER
DECLARE Hundreds, Tens, Units : INTEGER
Num <- 457
Hundreds <- Num DIV 100        // 4
Tens <- (Num MOD 100) DIV 10   // 5
Units <- Num MOD 10            // 7
OUTPUT Hundreds, Tens, Units   // Outputs: 4 5 7

DECLARE Last : INTEGER
Last <- 457 MOD 10
OUTPUT Last   // 7

DECLARE Rest : INTEGER
Rest <- 457 DIV 10
OUTPUT Rest   // 45

Five worked examples showing MOD and DIV in typical AS Level pseudocode.

Example 1 — check if a number is even or odd:

DECLARE Num : INTEGER
INPUT Num
IF Num MOD 2 = 0 THEN
  OUTPUT "Even"
ELSE
  OUTPUT "Odd"
ENDIF

Example 2 — extract individual digits from a 3-digit number:

DECLARE Num, H, T, U : INTEGER
Num <- 457
H <- Num DIV 100
T <- (Num MOD 100) DIV 10
U <- Num MOD 10
OUTPUT H, T, U   // 4 5 7

Example 3 — convert minutes to hours and minutes:

DECLARE TotalMin, Hours, Mins : INTEGER
TotalMin <- 135
Hours <- TotalMin DIV 60   // 2
Mins  <- TotalMin MOD 60   // 15
OUTPUT Hours, " hours ", Mins, " minutes"

Example 4 — check if a number is divisible by another:

DECLARE A, B : INTEGER
INPUT A
INPUT B
IF A MOD B = 0 THEN
  OUTPUT A, " is divisible by ", B
ELSE
  OUTPUT A, " is NOT divisible by ", B
ENDIF

Example 5 — reverse a 3-digit number using MOD and DIV:

DECLARE Num, Reversed : INTEGER
Num <- 123
Reversed <- (Num MOD 10) * 100            // 3 * 100 = 300
Reversed <- Reversed + ((Num DIV 10) MOD 10) * 10   // + 2 * 10 = 20
Reversed <- Reversed + (Num DIV 100)      // + 1
OUTPUT Reversed   // 321

A quick recap of everything you need to remember about MOD and DIV at AS Level.