Factor Calculator
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Find all factors and the prime factorization of any integer. Check if a number is prime.
Enter your values below and click Calculate for instant results.
The factors of a number are all the integers that divide into it evenly with no remainder. The factors of 12 are 1, 2, 3, 4, 6, and 12. Factors always come in pairs that multiply to give the original number: 1 and 12, 2 and 6, 3 and 4.
Every integer greater than 1 is either prime (has exactly two factors: 1 and itself) or composite (has more than two factors). The number 1 is neither prime nor composite by definition.
Prime factorization expresses a number as a product of prime numbers only. Every integer greater than 1 has exactly one prime factorization (ignoring the order of the factors). The prime factorization of 360 is 2^3 times 3^2 times 5, because 8 times 9 times 5 equals 360, and 2, 3, and 5 are all prime.
Factors are used in simplifying fractions (dividing numerator and denominator by their GCF), finding the least common multiple (needed for adding fractions with different denominators), solving algebraic equations through factoring, and in number theory and cryptography. The difficulty of factoring very large numbers into their prime factors is the foundation of much modern encryption.