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Factor Calculator

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Use this online factoring calculator that helps you to calculate factors of integers and polynomials. Enter a number and the tool will readily calculate prime, exponential, and paired factors without a delay.

How To Factor Polynomials?

If you are willing to know how to factor trinomials and binomials, using our factoring calculator with steps is the most suitable option for factoring quadratics. On the other hand, manual calculations can also be mastered if you continue reading!

How To Factor a Quadratic Equation?

Wondering about factoring a quadratic eqThe procedure is as same as factoring trinomials. The reason is that quadratic expression has 3 terms that make it a trinomial. The generic form of the second-degree equation is:

$$ ax^{2} + bx + c = 0 $$

Now if you think about how to factor quadratics in the above form, follow the technique below:

  • You need to look for two numbers such that their sum equals b and product equals ac.

$$ \left(number 1\right)*\left(number 2\right) = a*c $$

$$ \left(number 1\right) + \left(number 2\right) = b $$

  • At last, divide the middle term in the quadratic equation into the sum and product combination

$$ ax^{2} + \left(number 1\right))*x + \left(number 2\right)*x + c = 0 $$

Using our factoring trinomials calculator is an effective and recommended online way to factor any trinomials digitally.

How To Factor Trinomials?

Suppose you have an expression as:

$$ x^{2}+5x+6 $$

Following the procedure aforementioned, trinomial factoring is done as:

$$ x^{2}+3x+2x+6 $$

$$ x\left(x+3\right)+2\left(x+3\right) $$

$$ \left(x+2\right)\left(x+3\right) $$

These are the required factors and can also be checked using this factoring calculator with steps.

What Is a Factor of a Number?

“The number that divides an integer with no remainder at the end is called a factor”

Example:

If you need to find the factor numbers of 6, its factors would be 1, 2, 3, and 6. It means, 1, 2, 3, or 6 can be used to obtain "6". 

To instantly determine the factors of any number rather than only 6, you can enter it in this number factor calculator with steps and get detailed factors immediately. 

How To Find Factors of a Number?

If your goal comes up with manual calculations, then the following example will assist you to find all factors of a number:

Example: 

Calculate the possible factors of the integer 45.

Solution:

$$ \text{Total factors of 45} = 1, 3, 5, 9, 15, 45 $$

$$ \text{Prime factors of 45} = 3 × 3 × 5 $$

$$ \text{Exponential factors of 45} = 32 x 51 $$

$$ \text{Factor pairs of 45} = \left(1, 45\right), \left(3, 15\right), \left(5, 9\right) $$

Factor Divisibility Rules:

In finding the factor numbers of a number, certain rules help you out with accurate calculations. These include:

Number Factoring Rule
2 You may divide any even number by 2
3 You can only divide a number by 3 if the sum of individual digits in an original number is divisible by 3
4 You can divide a number by 4 if the last two individual digits are divisible by 4 in addition
5 You can divide numbers ending with 5 or 0 by 5
6 If a number is divisible by 2 and 3, you can also divide it by 6
7 To divide a number by 7, you have to go through the divisibility rule of 7
8 If the last 3 digits add and divisible by 8, the original number is also divisible by 8
9 You can divide a number by 9 if the sum of all individual digits is divisible by 9
10 You can only divide a number by 10 if it ends with 0

Facts About Factors:

  • You can not find out the factors of decimal numbers
  • Most of the odd numbers only have 1, or their own respective value as factors (Factors of 5 are 1, and 5 only)

To better calculate the factors that divide the number completely, you can do it now with our free factor generator.

Working of Factor Calculator:

Our factor finder automatically determines the necessary factors of a number and polynomial in moments. Let’s find how!

Input:

  • Select whether you wish to factor a number or polynomial
  • Enter the number or expression according to your choice
  • Tap Calculate

Output:

The factor tree calculator calculates

  • All possible factors to a positive or negative integer
  • Factors of a polynomial (binomial, trinomial, etc)

Some Important Factors:

With the help of a factoring calculator with steps, we have compiled some important factors in the table below to make your calculations easy:

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

References:

From the source Wikipedia: Factor

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