Factoring Calculator

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 this calculator.

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

You can use the factoring polynomials calculator to figure out the GCF in moments.

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 factoring trinomials 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.

Also, the prime factor calculator displays the factor tree corresponding to the given numbers.

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

Finding factor of a number becomes easy with the use of factor calculator. Here we have a detail example for clarification.

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

In case of large number, the calculation becomes very complex & difficult. Simply enter the value in factored form calculator which readily shows you the results.

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

However, our factor calculator also provides you with the factor expression by considering these properties.

Working of Factoring Calculator With Steps:

The factoring calculator 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.” For better understanding, you should use an online factor calculator that allows you to find the common factor of the given number.

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.