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**Table of Content**

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.

In mathematics:

**“Factoring is the technique to factor completely a number or a polynomial expression”**

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

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.

**“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.

What are the factors of 18 and 12?

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

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

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

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**”.

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 |

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.