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Euler's totient function is multiplicative, meaning $\varphi(nm) = \varphi(n)\varphi(m)$ whenever $\gcd(n, m) = 1$. In the prime factorization of $n$, the factors $p_i^{k_i}$ are powers of distinct primes.

Conditions: $n = p_1^{k_1}p_2^{k_2}\cdots p_m^{k_m}$ is the prime factorization of $n$.; $p_i$ are distinct prime numbers.; $\varphi$ is multiplicative for coprime integers.

Euler's totient function is multiplicative, meaning $\varphi(nm) = \varphi(n)\varphi(m)$ whenever $\gcd(n, m) = 1$. In the prime factorization of $n$, the factors $p_i^{k_i}$ are powers of distinct primes.

Conditions: $n = p_1^{k_1}p_2^{k_2}\cdots p_m^{k_m}$ is the prime factorization of $n$.; $p_i$ are distinct prime numbers.; $\varphi$ is multiplicative for coprime integers.