A multiplicative function is a type of arithmetic function that satisfies a specific property: if two numbers are coprime (they have no common factors other than 1), the function's value at the product of these numbers is equal to the product of the function's values at each number. In simpler terms, for a multiplicative function f , if a and b are coprime, then f(a \times b) = f(a) \times f(b) . Common examples of multiplicative functions include the Euler's totient function φ(n) and the divisor function d(n). These functions are important in number theory and have applications in areas such as cryptography and the study of prime numbers. Understanding multiplicative functions helps in analyzing the properties of integers and their relationships.