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Math Calculators ▶ Factoring Calculator

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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 this calculator.

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

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

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.

**“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.

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

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

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.

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.

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

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.

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.