Factoring Calculator

This calculator finds all the factors of a whole number, lists its factor pairs, tells you whether it is prime, and gives its prime factorisation. Factors, also called divisors, are the whole numbers that divide evenly into a number with no remainder, and finding them is a basic but constant task in mathematics, from simplifying fractions and finding common denominators to solving problems in number theory and cryptography. Doing it by hand means testing divisors one by one, which is slow and easy to get wrong, especially for larger numbers where it is hard to be sure you have found them all. This tool does it instantly and completely. You enter a whole number and the calculator lists every factor in order, pairs them up into the factor pairs that multiply to give the number, states whether the number is prime, which means it has exactly two factors, one and itself, and shows the prime factorisation, the unique way of writing the number as a product of prime numbers. The prime factorisation is particularly useful, since it underlies the highest common factor and lowest common multiple and much of number theory. The results update as you type. Use it to check homework, to simplify fractions, to find common factors and multiples, or to explore which numbers are prime. The calculator handles reasonably large numbers efficiently; very large numbers are limited to keep it fast and the output readable. The results are exact for whole-number inputs.

Factors are whole numbers that divide evenly with no remainder. A prime has exactly two factors. Large numbers are capped for speed.