Find all factors and factor pairs of any number. Enter a number to see its complete list of divisors.
Find the prime factorization of any number. See the step-by-step breakdown and factor tree represent…
Find the GCF (Greatest Common Factor) of two or more numbers using prime factorization or the Euclid…
Find the LCM (Least Common Multiple) of two or more numbers. See step-by-step solutions using the pr…
Find all common factors between two or more numbers. See which divisors are shared and identify the …
In multiplication, factors are the integers that are multiplied together to find other integers. For example, 6 × 5 = 30. In this example, 6 and 5 are the factors of 30. 1, 2, 3, 10, 15, and 30 would also be factors of 30. Essentially, an integer a is a factor of another integer b, so long as b can be divided by a with no remainder. Factors are important when working with fractions, as well as when trying to find patterns within numbers.
Prime factorization involves finding the prime numbers that, when multiplied, return the number being addressed. For example, prime factorization of 120 results in 2 × 2 × 2 × 3 × 5. It can be helpful to use a factor tree when computing the prime factorizations of numbers. Using 120:
120
/ \
2 60
/ \
2 30
/ \
2 15
/ \
3 5From the simple example of 120, it is clear that prime factorization can become quite tedious fairly quickly. Unfortunately, there is currently no known algorithm for prime factorization that is efficient for very large numbers. Many calculators, including the one on this page, cannot calculate prime factorizations beyond a certain magnitude. One concerted effort between several researchers to factor RSA-768, a 232-digit number, took 2 years using hundreds of machines.
Although no efficient algorithm has been found, it also has yet to be proven that no such algorithm exists, leaving room for anyone interested in having their name in a mathematical algorithm to formulate one (or prove in some self-named theorem that one doesn't exist)!