A multiplicative function is a special type of function in number theory 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 mathematical terms, if f is a multiplicative function and a and b are coprime, then f(ab) = f(a) \cdot f(b) . Common examples of multiplicative functions include the Euler's totient function φ(n) and the divisor function d(n). These functions play a significant role in various areas of number theory, including the study of prime numbers and the distribution of integers. Understanding multiplicative functions helps mathematicians analyze the properties of numbers and their relationships.