Trial Division
Trial division is a simple, deterministic algorithm for integer factorization and primality testing that involves systematically dividing a number by all integers from 2 up to its square root. It checks if any of these divisions result in an integer quotient, indicating a factor, or if none do, confirming the number is prime. While straightforward and easy to implement, it is computationally inefficient for large numbers due to its linear time complexity relative to the input size.
Developers should learn trial division as a foundational concept in number theory and algorithm design, particularly for educational purposes, small-scale applications, or when implementing basic cryptographic or mathematical functions. It is useful in scenarios like verifying prime numbers in low-security contexts, teaching algorithmic thinking, or as a benchmark for more advanced factorization methods such as the Sieve of Eratosthenes or Pollard's rho algorithm.