Factor Calculator

A factor is a whole number that divides evenly into another number with no remainder. For example, 1, 2, 3, 4, 6, and 12 are all factors of 12 because each one divides into 12 without leaving a remainder.

Prime factorization is the process of expressing a number as a product of its prime number components. For example, the prime factorization of 120 is 2 × 2 × 2 × 3 × 5 (or 2³ × 3 × 5). Every integer greater than 1 has a unique prime factorization.

Factor pairs are two numbers that, when multiplied together, produce the original number. For example, the factor pairs of 12 are (1, 12), (2, 6), and (3, 4). Each pair consists of two factors whose product equals the number you entered.

This calculator works with positive integers. For negative integers, the factor pairs include both negative and positive combinations — for example, factors of -6 include (-1, 6), (1, -6), (-2, 3), and (2, -3).

Factors divide evenly into a number, while multiples are the results of multiplying a number by integers. For example, factors of 6 are 1, 2, 3, and 6, whereas multiples of 6 are 6, 12, 18, 24, and so on.

A prime number has exactly two factors: 1 and itself. If the calculator shows a factor count of 2, the number is prime. Examples include 2, 3, 5, 7, 11, and 13.

Factors are essential when simplifying fractions, finding the greatest common factor (GCF) or least common multiple (LCM), solving algebraic expressions, and identifying number patterns. They form the foundation for many areas of arithmetic and algebra.

The calculator checks every integer from 1 up to the square root of your number. If a number divides evenly, both it and its corresponding pair are recorded as factors. This ensures all factors are found efficiently without checking every number up to the input.