Factor Calculator

This factor calculator generates the prime factorization of a given number. Enter an integer and the tool will factoring calculator will generate a list of factors, separated by commas.

These can also be expressed as factor pairs by dividing the integer by its factor . So the integer 10 can be factored into 5, 2, and 1. The factor pairs of this integer are: (10,1), (5,2).

Given that multiplication yields the same result, you don't need to repeat factor pairs.

What is a prime factorization?

The prime factorization of a integer number is the set of prime number factors which will equal that number if multiplied together. Prime numbers are numbers which can only be divided by themselves and zero; thus a prime number factorization breaks an integer number down to its fundamental elements (prime factor).

Our factor detail pages include a prime factorization calculator specific to each factor. See the links below for an example. We determine this using an iterative algorithm.

What is a factor tree?

A factor tree is a visual approach to showing each step of the calculation behind the factors of an integer number as a tree diagram. Starting with the original number, you break the integer into factor pairs. From there, you break each factor pairs into an appropriate sub-factor. (so 54 = 2 x 27 => 27 becomes 3 x 9 => 3 x 3 ). It's good form to include parentheses if you're repeating a factor.

In short, a factor tree is a good way to organize your manual calculation for a test.

What is the greatest common factor (gcf)?

The greatest common factor of an integer is the highest integer which is a factor of both numbers. This can be derived from the primar factors of the two numbers; note that you should multiply common prime factors together (including repeating them) if present for both numbers in similar quantities. For example, consider the greatest common divisor of 81 (which can be written as 3 to the quadratic power) and 27 (3 cubed) is 27... since the greatest common factor is 3 x 3 x 3 = 27.

We've got another calculator to identify the greatest common factor (to help with checking that part of your homework)... The greatest common factor is also the greatest common divisor of the two numbers.

Are Negative Factors possible?

Yes but these are generally limited to higher level college mathematics. Any negative number would have -1 as a factor. Both positive factors and negative factors are referred to as the factors. This should be sufficient for most problem sets below the college level; factors are expressed as a positive integer / positive number.

The difference starts once you get into advanced algebra and calculus, you've got other options including imaginary numbers (square root of negative 1). Abstract algebra introduces other complexity, in the sense you can start redefining how number systems work and the underlying topology.

What about factoring a polynomial function?

We're working on another version of the factoring calculator for algebraic expressions and quadratic equation problems. This is where you are splitting up a variable expression and function formula.