Remainder and Exponentiation

Remainder and Exponentiation

Two special math tools: the remainder operator % and the power function pow().

The remainder operator

% gives what is left over after a division. 7 % 3 is 1: three goes into seven two whole times, and 1 is left.

cout << 7 % 2 << endl;   // 1
cout << 7 % 3 << endl;   // 2
cout << 12 % 6 << endl;  // 0

A great trick: checking even numbers

x % 2 == 0 is true exactly when x is even. That is one of the most used patterns in C++.

int x = 8;
bool isEven = (x % 2 == 0);  // true

Division team: quotient and remainder

10 / 4 is the quotient (2) and 10 % 4 is the remainder (2). Together they cover everything a division leaves behind.

Exponentiation with pow

C++ has no power symbol. 2 ^ 3 means something else in C++! For powers, use pow(base, exponent) from the <cmath> header:

#include <cmath>
using namespace std;

cout << pow(2, 4) << endl;  // 16
cout << pow(3, 2) << endl;  // 9

Inside pow(x, y), the first number is the base and the second is the exponent, so pow(2, 4) means 2 2 2 * 2. pow returns a double, so the result can have decimals.

TL;DR

• % gives the remainder of a division.
• Check even numbers with x % 2 == 0.
• Do not use ^ for powers in C++.
• Use pow(base, exponent) from <cmath> for exponents.