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Factoring Calculator

Enter any polynomials or a non-zero integer and the tool will instantly reduce it to simple factor pairs.

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Factoring calculator helps to factor any integer (positive or negative) and expression like polynomial, binomial, trinomial. You can easily transform complex expressions and numbers into a product of simpler factors by using the calculator. Calculate factor tree and get step by step calculations.

What Is Factoring?

In mathematics: “Factoring is the technique to factor completely a number or a polynomial expression”

How To Factor Polynomials?

Factoring Polynomials is an important process that can be done by simple steps as follows:
  • Look for the greatest common factor (GCF) in the given polynomial expression
  • If we found the greatest common factor, then factor it out of polynomial

How to Factor Trinomials?

Trinomial factorization is the technique of multiplying two binomial factors. The generic form of trinomial is the second degree equation and it given as: \(ax^{2}+bx+c\) Let’s consider an example: (x+2)(x+6) x(x+2)+2(x+2) x^2+6x+2x+12 x^2+8x+12 Even though this method helps to find answers without going through so many steps, but the calculator helps you to find a factor of trinomials in a very simple way by just entering an expression.

What Is a Factor of a Number?

“The factors of a number are referred to as the numbers that divide into it exactly” For example, The number 15 has 3 and 5 factors, because: 3×5 = 15 Remember that some numbers have more than one factorization (means more than one way of being factored). For example, 24 contains six factors: 1, 2, 3, 4, 6, 8, 12, and 24, so you get 1×24, 2×12, 3×8, or 4×6. So, if 24 is divided by any of these eight factors then the answer you will get is a whole number.

How to Find Factors (Step-by-Step):

Example:

What are the factors of 18 and 12?

Solution:

The factors of 18 = 1, 2, 3, 6, 9, 18 The factors of 12 = 1, 2, 3, 4, 6, 12 Prime factors of 18 = 2 × 3 × 3 Prime factors of 12 = 2 × 2 × 3 Factor pairs of 18 = (3, 6), (2, 9), (1, 18) Factor pairs of 12 = (2, 6), (3, 4), (1, 12) There are 4 common factors in both numbers. 1,2,3,6

Properties of Factor:

These are the properties of factor:
  • 1 is the factor for every number
  • Every number consists of the factor of itself
  • Every factor is less than or equal to the given number
  • There are also a finite number of factors

Working of Factoring Calculator:

The tool is 100% free and instantly finds the factors of any number and algebraic polynomial expressions. Let’s find out what you need to do! Input:
  • Make your choice (Either “Integer Factoring” or "Polynomial Factoring”)
  • Now enter the number or expression according to your choice
  • Tap Calculate
Output: The factorization calculator automatically determines the following results:
  • Factors of an algebraic expression
  • Factors of a number
  • Prime factors of a number
  • Factor pairs of the numbers
  • Common factors between the number
  • Prime factor tree of the number

FAQ's:

What Is a Common Factor?

When it comes to finding the factors of two or more numbers, and then to find the factors that are the same (common), they are referred to as the “common factors”.

Factors of Common Numbers:

Let's take a look at the given table:
Common Numbers Factor of numbers
1 1
2 1, 2
3 1, 3
4 1, 2, 4
5 1, 5
6 1, 2, 3, 6
7 1, 7
8 1, 2, 4, 8
9 1, 3, 9
10 1, 2, 5, 10
11 1, 11
12 1, 2, 3, 4, 6, 12
13 1, 13
14 1, 2, 7, 14
15 1, 3, 5, 15
16 1, 2, 4, 8, 16
17 1, 17
18 1, 2, 3, 6, 9, 18
19 1, 19
20 1, 2, 4, 5, 10, 20
21 1, 3, 7, 21
22 1, 2, 11, 22
23 1, 23
24 1, 2, 3, 4, 6, 8, 12, 24
25 1, 5, 25
26 1, 2, 13, 26
27 1, 3, 9, 27
28 1, 2, 4, 7, 14, 28
29 1, 29
30 1, 2, 3, 5, 6, 10, 15, 30
31 1, 31
32 1, 2, 4, 8, 16, 32
33 1, 3, 11, 33
34 1, 2, 17, 34
35 1, 5, 7, 35
36 1, 2, 3, 4, 6, 9, 12, 18, 36
37 1, 37
38 1, 2, 19, 38
39 1, 3, 13, 39
40 1, 2, 4, 5, 8, 10, 20, 40
41 1, 41
42 1, 2, 3, 6, 7, 14, 21, 42
43 1, 43
44 1, 2, 4, 11, 22, 44
45 1, 3, 5, 9, 15, 45
46 1, 2, 23, 46
47 1, 47
48 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
49 1, 7, 49
50 1, 2, 5, 10, 25, 50
51 1, 3, 17, 51
52 1, 2, 4, 13, 26, 52
53 1, 53
54 1, 2, 3, 6, 9, 18, 27, 54
55 1, 5, 11, 55
56 1, 2, 4, 7, 8, 14, 28, 56
57 1, 3, 19, 57
58 1, 2, 29, 58
59 1, 59
60 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
61 1, 61
62 1, 2, 31, 62
63 1, 3, 7, 9, 21, 63
64 1, 2, 4, 8, 16, 32, 64
65 1, 5, 13, 65
66 1, 2, 3, 6, 11, 22, 33, 66
67 1, 67
68 1, 2, 4, 17, 34, 68
69 1, 3, 23, 69
70 1, 2, 5, 7, 10, 14, 35, 70
71 1, 71
72 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
73 1, 73
74 1, 2, 37, 74
75 1, 3, 5, 15, 25, 75
76 1, 2, 4, 19, 38, 76
77 1, 7, 11, 77
78 1, 2, 3, 6, 13, 26, 39, 78
79 1, 79
80 1, 2, 4, 5, 8, 10, 16, 20, 40, 80
81 1, 3, 9, 27, 81
82 1, 2, 41, 82
83 1, 83
84 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
85 1, 5, 17, 85
86 1, 2, 43, 86
87 1, 3, 29, 87
88 1, 2, 4, 8, 11, 22, 44, 88
89 1, 89
90 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90
91 1, 7, 13, 91
92 1, 2, 4, 23, 46, 92
93 1, 3, 31, 93
94 1, 2, 47, 94
95 1, 5, 19, 95
96 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96
97 1, 97
98 1, 2, 7, 14, 49, 98
99 1, 3, 9, 11, 33, 99
100 1, 2, 4, 5, 10, 20, 25, 50, 100
104 1, 2, 4, 8, 13, 26, 52, 104
110 1, 2, 5, 10, 11, 22, 55, 110
120 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
121 1, 11, 121
126 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126
135 1, 3, 5, 9, 15, 27, 45, 135
147 1, 3, 7, 21, 49, 147
162 1, 2, 3, 6, 9, 18, 27, 54, 81, 162
175 1, 5, 7, 25, 35, 175
189 1, 3, 7, 9, 21, 27, 63, 189
196 1, 2, 4, 7, 14, 28, 49, 98, 196
210 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210
225 1, 3, 5, 9, 15, 25, 45, 75, 225
245 1, 5, 7, 35, 49, 245
256 1, 2, 4, 8, 16, 32, 64, 128, 256
288 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96, 144, 288
300 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 300
360 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360
375 1, 3, 5, 15, 25, 75, 125, 375
400 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400
500 1, 2, 4, 5, 10, 20, 25, 50, 100, 125, 250, 500
625 1, 5, 25, 125, 625

Reference:

From the source of Wikipedia: Expressions, History of factorization of expressions, Common factor, Grouping. From the source of Mesacc: Factoring Strategies, Adding and subtracting terms, Binomial expansions.
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