Find all factors, factor pairs, and prime factors of any positive integer
This factor calculator finds all positive divisors of any positive integer. It displays the complete list of factors, factor pairs, prime factorization, and indicates whether the number is prime. Understanding factors is fundamental to number theory and algebra.
Factors of a number are positive integers that divide the number evenly (with no remainder). For example, the factors of 12 are 1, 2, 3, 4, 6, and 12. Factor pairs are pairs of numbers that multiply together to give the original number, such as (1,12), (2,6), and (3,4).
Test each integer from 1 up to the square root of the number. If the number is divisible evenly, record both the divisor and the quotient. This gives you all factor pairs efficiently without needing to test every number up to the target.
A prime factor is a factor that is itself a prime number. Prime factorization expresses a number as a product of prime numbers only. For example, 84 = 2² × 3 × 7. Every integer greater than 1 has a unique prime factorization (Fundamental Theorem of Arithmetic).