# Euler's totient function ## Synopsis **Euler's totient function** counts the positive integers up to a given integer n that are relatively prime to n. It is written using the Greek letter *phi* as $\varphi (n)$ or $\phi(n)$, and may also be called **Euler's phi function**. In other words, it is the number of integers k in the range 1 ≤ _k_ ≤ _n_ for which the greatest common divisor gcd(_n_, _k_) is equal to 1.