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.
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!
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:
$$ \left(number 1\right)*\left(number 2\right) = a*c $$
$$ \left(number 1\right) + \left(number 2\right) = b $$
$$ ax^{2} + \left(number 1\right))*x + \left(number 2\right)*x + c = 0 $$
Using our factoring trinomials calculator is an effective and recommended online way to factor any trinomials digitally.
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.
“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.
If your goal comes up with manual calculations, then the following example will assist you to find all factors of a number:
Calculate the possible factors of the integer 45.
$$ \text{Total factors of 45} = 1, 3, 5, 9, 15, 45 $$
$$ \text{Prime factors of 45} = 3 × 3 × 5 $$
$$ \text{Exponential factors of 45} = 32 x 51 $$
$$ \text{Factor pairs of 45} = \left(1, 45\right), \left(3, 15\right), \left(5, 9\right) $$
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 |
To better calculate the factors that divide the number completely, you can do it now with our free factor generator.
Our factor finder automatically determines the necessary factors of a number and polynomial in moments. Let’s find how!
Input:
Output:
The factor tree calculator calculates
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 |
From the source Wikipedia: Factor
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