Check divisibility by small primes first: 2, 3, 5, 7, 11, 13, 17, 19
Use the sum of digits rule for divisibility by 3 and 9
Check the last digit for divisibility by 2 and 5
Test divisibility up to the square root of the number
Divide the number by each possible factor and record exact divisors
Use prime factorization to break the number into prime factors
Build all factors from the prime factors
Use factor pairs: if a divides n, then n ÷ a is also a factor
Apply trial division with increasing primes
Use a factor tree to organize repeated division
Use modular arithmetic to test divisibility quickly
Use a calculator or computer for large candidates
Use Pollard’s Rho for large composite numbers
Use Fermat’s factorization when the number is near a perfect square
Use the greatest common divisor with related numbers if available
Stop once the quotient becomes smaller than the tested factor
Include 1 and the number itself as factors