Factor Calculator
Please provide an integer to calculate its factors and prime factors.
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, the 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:
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)!
Frequently Asked Questions
What is a factor?
An integer a is a factor of another integer b if b can be divided by a with no remainder. The factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30 — each of them divides 30 exactly.
What is prime factorization?
Prime factorization expresses a number as the product of prime numbers: 120 = 2 × 2 × 2 × 3 × 5. Every integer greater than 1 has exactly one prime factorization, which is why it is sometimes called the fundamental theorem of arithmetic.
What is a factor tree?
A factor tree breaks a number down step by step: write the number, split off one factor pair, and keep splitting the composite parts until every branch ends in a prime. For 120: 120 = 60 × 2, 60 = 30 × 2, 30 = 15 × 2, 15 = 5 × 3.
How many factors does a number have?
From the prime factorization: if n = pa × qb × …, the number of factors is (a+1)(b+1)… For 120 = 23 × 3 × 5 that is 4 × 2 × 2 = 16 factors. A prime number has exactly 2 factors: 1 and itself.