# Factor Calculator Factor calculator is a tool that helps in finding the factors of a given number. It is commonly used in mathematics and is beneficial for various purposes, such as solving equations, simplifying fractions, and determining prime numbers.

Related

## What is a factor?

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    5

From 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)!

## Factor Calculator Example

Number Factors
12 1, 2, 3, 4, 6, 12
24 1, 2, 3, 4, 6, 8, 12, 24
32 1, 2, 4, 8, 16, 32
45 1, 3, 5, 9, 15, 45
60 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

In this table, the "Number" column represents the input number for which we want to find the factors. The "Factors" column lists all the factors of each respective number, separated by commas.

For example, the factors of 12 are 1, 2, 3, 4, 6, and 12. Similarly, the factors of 24 include 1, 2, 3, 4, 6, 8, 12, and 24. The factors of 32 are 1, 2, 4, 8, 16, and 32. For the number 45, the factors are 1, 3, 5, 9, 15, and 45. Lastly, the factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.

Using a Factor Calculator can significantly simplify the process of finding all the factors of a given number. It can be particularly useful in mathematics, prime factorization, and solving various numerical problems.