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.

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.

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.

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.

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.

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.

This tool can also be used to generate lists of specific factors that can be shared via url. Here are some common requests:

- Factors of 1
- Factors of 36
- Factors of 24
- Factors of 48
- Factors of 72
- Factors of 42
- Factors of 30
- Factors of 60
- Factors of 45
- Factors of 18
- Factors of 32
- Factors of 12
- Factors of 56
- Factors of 40
- Factors of 28
- Factors of 54
- Factors of 63
- Factors of 16
- Factors of 20
- Factors of 21
- Factors of 35
- Factors of 49
- Factors of 75
- Factors of 90
- Factors of 120
- Factors of 96
- Factors of 25
- Factors of 84
- Factors of 80
- Factors of 81
- Factors of 70
- Factors of 144
- Factors of 14
- Factors of 26
- Factors of 98
- Factors of 180
- Factors of 52
- Factors of 39
- Factors of 9
- Factors of 10
- Factors of 34
- Factors of 33
- Factors of 65
- Factors of 150
- Factors of 91
- Factors of 22
- Factors of 112
- Factors of 225
- Factors of 147
- Factors of 29
- Factors of 41
- Factors of 105
- Factors of 128
- Factors of 125
- Factors of 216
- Factors of 196
- Factors of 55
- Factors of 85
- Factors of 121
- Factors of 80
- Factors of 38
- Factors of 126
- Factors of 192
- Factors of 37
- Factors of 68
- Factors of 31
- Factors of 66
- Factors of 17
- Factors of 240
- Factors of 99
- Factors of 140
- Factors of 200
- Factors of 168
- Factors of 78
- Factors of 135
- Factors of 169
- Factors of 160
- Factors of 46
- Factors of 77
- Factors of 47
- Factors of 76
- Factors of 210
- Factors of 300
- Factors of 256
- Factors of 252
- Factors of 89

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