The Modulus (%) Operator in C++

This is a quick lesson on the Modulus Operator, which will return the "remainder" of dividing two integers.

This might seem quite niche, but turns out to be incredibly useful for programming.

We can imagine that the answer to a division question like $5 \div 3$ might be $1$, with $2$ left over.

$1$ is the quotient and $2$ is the remainder.

We've previously seen how the division operator, / lets us get the quotient:

1// This will be 1
2int Quotient { 5 / 3 };
3

The modulus operator, denoted by the % character, is how we get the remainder:

1// This will be 2
2int Remainder { 5 % 3 };
3

The modulus operator is only used with integers, and almost exclusively positive integers. Because of this, the return type of the modulus operator will also be an integer.

A common use of the modulus operator to check if a number is even. Only even numbers have no remainder after being divided by $2$:

1bool isEven(int Number) {
2  return Number % 2 == 0;
3}
4

1int Remainder { 5 % 6 };
2

Modulus Operator With Loops

Lets consider some more examples of what the modulus operator will return:

1int Result0 { 0 % 3 }; // 0
2int Result1 { 1 % 3 }; // 1
3int Result2 { 2 % 3 }; // 2
4
5int Result3 { 3 % 3 }; // 0
6int Result4 { 4 % 3 }; // 1
7int Result5 { 5 % 3 }; // 2
8
9int Result6 { 6 % 3 }; // 0
10int Result7 { 7 % 3 }; // 1
11int Result8 { 8 % 3 }; // 2
12
13int Result9 { 9 % 3 }; // 0
14int Result10 { 10 % 3 }; // 1
15int Result11 { 11 % 3 }; // 2
16

We can see a repeating pattern developing here as we increment the left operand.

1i++;
2

This repeating pattern is the main reason modulus is useful in programming - particularly when paired with loops.

For example, if we wanted to do something on every 10th iteration of a loop:

1for (int i = 1; i <= 50; i++) {
2  cout << i << " ";
3  if (i % 10 == 0) cout << endl;
4}
5

The above code inserts an endl on every 10th iteration. The output looks like this:

11 2 3 4 5 6 7 8 9 10 
211 12 13 14 15 16 17 18 19 20 
321 22 23 24 25 26 27 28 29 30 
431 32 33 34 35 36 37 38 39 40 
541 42 43 44 45 46 47 48 49 50
6

The next lesson introduces a challenge where the modulus operator is very helpful.