Euler's totient function, denoted as φ(n), counts the positive integers up to a given integer n that are relatively prime to n. Two numbers are considered relatively prime if their greatest common divisor (GCD) is 1. For example, φ(9) equals 6 because the numbers 1, 2, 4, 5, 7, and 8 are all relatively prime to 9. This function is significant in number theory and has applications in areas such as cryptography, particularly in algorithms like RSA. The value of φ(n) can be calculated using the prime factorization of n, making it a useful tool for understanding the properties of integers.