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Math Calculators ▶ Factor Calculator
An online factor calculator allows you to find the factors and pairs of factors of a positive or negative number. When it comes to positive numbers, the factorization calculator will only show you the positive factors. For example, you get 4 & 2 as the factor pair of 8, if you want to get the negative factors. And, for negative factors, you have to duplicate the answer and simply repeat all of the factors with negatives (-) such as -4 & -2 as another pair of 8. Quit worrying, this factors calculator helps to factor the negative numbers as well as positive numbers. For example: -4 & 2 AND 4 & -2 are both the factor pair of -8.
Apart from manual calculations, thanks to factored form calculator that provides you the factored form of a number of your choice.
So, we decided to explain how to find factors (step-wise), and by using factor finder and table for common numbers and much more. Let’s start exploring some basics!
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 have 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 tree calculator displays the factor tree corresponding to the given numbers.
These are the properties of factor:
However, this online factor calculator also provides you the factor expression by considering these properties.
Finding factor of a number become very easy with the assistance of this factorization calculator. Here we have a detail example for clarification. Also, you can try a factors calculator that helps you to find all possible factors of a number.
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 this factored form calculator which readily shows you the results.
By using the online factor finder, it’s become easy to find the factors of any number with their factor pairs. Simply stick to the following instructions!
Inputs:
Outputs:
The factored form calculator shows:
Also, you can try our online prime factorization calculator that helps you to determine the prime factors of any number you want with complete calculation.
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.
Typically, factors are given as pairs of numbers that multiply together to provide the original number. These are said to be as the factor pairs.
Simply, both 2 and x are the factors of 2x.
You can use the equation solver function to factor on a TI-84 calculator. If you need to access it, then follow the given steps:
Also, you can be able to add a custom program to your calculator to easily do factor polynomials calculation.
The number has exactly 3 factors when it is a square of a prime number. For example, the factors of 9 are 1, 3, and 9, and the factors of 49: 1, 7, and 49.
Understanding the factors helps you to easily navigate the relationship between the numbers in real world without dependent on the calculator or phone. This concept is widely useful for the K-12 Education as well as for the professionals. For the calculation of large number, it’s very daunting task to do calculations by hand. For ease, simply try an online factor calculator that helps to solve the factor problems within no time.
Lets 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 authorized source of Wikipedia : Definition and general introduction of factorization
From the site of Sciencing.com : How do I use factors in real world
From the source of purplemath : How to find factors manually
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