Factor Calculator
With this factor calculator, you will determine the factors of any positive natural number. A factor is any number that divides evenly into another number.
Just enter any positive integer, and in the blink of an eye you'll find all positive factors of that number. If you are not sure what a factor is, scroll down to find the factor definition, as well as divisibility rules with a dedicated paragraph for not so wellknown divisibility rule of 7.
What is a factor?/Factor definition
A factor, also called a divisor, is any number that divides evenly into another number. In other words, factors are the numbers we can multiply together to get a certain product:
You can also notice that dividing the product by its factor leaves no remainder.
Definition of the factor differs: some definitions claim that factor can be negative as well as positive, but in other cases, the term is restricted to positive factors only.
For example, the factors of 8
are 1, 2
, 4
and 8
. But, from the other hand, if you multiply 2
times 4
, you'll also obtain 8
, therefore 2
and 4
are factors of 8
according to the first definition.
Technically, you can have negative factors, although it's not so popular to use them. For practical purposes, our factor calculator provides only positive factors. If you need negative ones for some reason, just add the minus in front of every obtained value:
Factors of 8 are: 1, 2, 4, 8
plus 1, 2, 4, 8
as well.
Divisibility rules
There are many rules of divisibility that greatly assist one in finding factors by hand. The most often used ones are:

2: Any even number is divisible by
2
. 
3: A number is divisible by
3
if the sum of the digits in the number is divisible by3
. 
4: A number is divisible by
4
if the last two digits form a number that is divisible by4
. 
5: Any number ending in
5
or0
is divisible by5
. 
6: A number is divisible by
6
if it is divisible by2
and3
. 
7: The divisibility rule of
7
also exists, but it's a bit more complicated. Find a short paragraph below. 
8: If the last three digits form a number that is divisible by
8
, then the entire number is divisible by8
. 
9: If the sum of the digits is divisible by
9
, the entire number is divisible by9
. 
10: Any number ending in
0
is divisible by10
.
There are many aspects of mathematics where it's important to be able to find the factors. The factor calculator is helpful in finding the greatest common factor, least common multiple and prime factorization.
Divisibility rule of 7
Want to check if 7 is a factor of our number? There are two basic methods for testing that. Let's show it on the example of a number 13468.

Method 1
 Take the last digit. It's 8 in our case.
 Double the last digit. 2 * 8 = 16.
 Take the remaining digits (truncated number). For us  1346.
 Find the difference between the number from remaining digits and doubled last digit. Which means, we need to subtract 16 from 1346.
1346  16 = 1330
.  Continue to do this procedure until a number known to be divisible by 7 (or not) is obtained. We don't know straight away if
1330
is divisible by 7, so we repeat the steps all over again:

0

0

133

133  0 = 133
Is
133
divisible by 7? Not sure, so repeat the procedure once more: 
3

6

13

13  6 = 7
Great! We obtained the number divisible by 7, so it means that our original number 13468 is also divisible by 7.

Method 2

Take the digits of the number in reverse order. So for our original number 13468, we have 8 6 4 3 1.

Multiply them successively by the digits 1, 3, 2, 6, 4, 5. Repeat or shorten this sequence to the necessary length. So in our case, we get:
8 * 1, 6 * 3, 4 * 2, 3 * 6 and 1 * 4.

Add the obtained products. If the result is divisible by 7, then the original number is as well. So:
(8 * 1) + (6 * 3) + (4 * 2) + (3 * 6) + (1 * 4) = 8 + 18 + 8 + 18 + 4 = 56
, which is a number divisible by 7.

Other related areas of interest
Prime factorization is an extension of factorization in which all the factors are prime numbers. For example, suppose we want the prime factorization of 48
. The factors of 48
are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
. Notice those are not all prime numbers, so we have to break it down further. When completing the process, we get 2 * 2 * 2 * 2 * 3
. Although 1
is a factor, many mathematicians now do not consider 1
to be a prime number. The prime factorization calculator is a handy tool to obtain these factors.
Another area of interest is calculating the greatest common factor (GCF) of a set of numbers. To do so, we get the prime factorization of all the numbers. Then multiply all the factors that are the same in each set. For example, suppose we want the GCF of 24
, 44
and 68
. The prime factorizations are 24 = 2 * 2 * 2 * 3
, 44 = 2 * 2 * 11
and 68 = 2 * 2 * 17
. Notice the only number present in all sets of factors is 2
, which appears in common twice, so the GCF is 2 * 2 = 4
. The GCF calculator will provide this result simply and quickly.
Closely related to the GCF is the least common multiple, abbreviated as LCM. The process is as follows: we get the prime factorizations and multiply the highest power of all factors present. In the example above, the LCM would be 2 * 2 * 2 * 3 * 11 * 17 = 4488
. The use of the least common multiple calculator will make a sometimes tedious process much easier.
What are the factors of...
You can use the factor calculator to obtain the list of factors below:
 Factors of 1: 1
 Factors of 2: 1, 2
 Factors of 3: 1, 3
 Factors of 4: 1, 2, 4
 Factors of 5: 1, 5
 Factors of 6: 1, 2, 3, 6
 Factors of 7: 1, 7
 Factors of 8: 1, 2, 4, 8
 Factors of 9: 1, 3, 9
 Factors of 10: 1, 2, 5, 10
 Factors of 11: 1, 11
 Factors of 12: 1, 2, 3, 4, 6, 12
 Factors of 13: 1, 13
 Factors of 14: 1, 2, 7, 14
 Factors of 15: 1, 3, 5, 15
 Factors of 16: 1, 2, 4, 8, 16
 Factors of 17: 1, 17
 Factors of 18: 1, 2, 3, 6, 9, 18
 Factors of 19: 1, 19
 Factors of 20: 1, 2, 4, 5, 10, 20
 Factors of 21: 1, 3, 7, 21
 Factors of 22: 1, 2, 11, 22
 Factors of 23: 1, 23
 Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
 Factors of 25: 1, 5, 25
 Factors of 26: 1, 2, 13, 26
 Factors of 27: 1, 3, 9, 27
 Factors of 28: 1, 2, 4, 7, 14, 28
 Factors of 29: 1, 29
 Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
 Factors of 31: 1, 31
 Factors of 32: 1, 2, 4, 8, 16, 32
 Factors of 33: 1, 3, 11, 33
 Factors of 34: 1, 2, 17, 34
 Factors of 35: 1, 5, 7, 35
 Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
 Factors of 37: 1, 37
 Factors of 38: 1, 2, 19, 38
 Factors of 39: 1, 3, 13, 39
 Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40
 Factors of 41: 1, 41
 Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42
 Factors of 43: 1, 43
 Factors of 44: 1, 2, 4, 11, 22, 44
 Factors of 45: 1, 3, 5, 9, 15, 45
 Factors of 46: 1, 2, 23, 46
 Factors of 47: 1, 47
 Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
 Factors of 49: 1, 7, 49
 Factors of 50: 1, 2, 5, 10, 25, 50
 Factors of 51: 1, 3, 17, 51
 Factors of 52: 1, 2, 4, 13, 26, 52
 Factors of 53: 1, 53
 Factors of 54: 1, 2, 3, 6, 9, 18, 27, 54
 Factors of 55: 1, 5, 11, 55
 Factors of 56: 1, 2, 4, 7, 8, 14, 28, 56
 Factors of 57: 1, 3, 19, 57
 Factors of 58: 1, 2, 29, 58
 Factors of 59: 1, 59
 Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
 Factors of 61: 1, 61
 Factors of 62: 1, 2, 31, 62
 Factors of 63: 1, 3, 7, 9, 21, 63
 Factors of 64: 1, 2, 4, 8, 16, 32, 64
 Factors of 65: 1, 5, 13, 65
 Factors of 66: 1, 2, 3, 6, 11, 22, 33, 66
 Factors of 67: 1, 67
 Factors of 68: 1, 2, 4, 17, 34, 68
 Factors of 69: 1, 3, 23, 69
 Factors of 70: 1, 2, 5, 7, 10, 14, 35, 70
 Factors of 71: 1, 71
 Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
 Factors of 73: 1, 73
 Factors of 74: 1, 2, 37, 74
 Factors of 75: 1, 3, 5, 15, 25, 75
 Factors of 76: 1, 2, 4, 19, 38, 76
 Factors of 77: 1, 7, 11, 77
 Factors of 78: 1, 2, 3, 6, 13, 26, 39, 78
 Factors of 79: 1, 79
 Factors of 80: 1, 2, 4, 5, 8, 10, 16, 20, 40, 80
 Factors of 81: 1, 3, 9, 27, 81
 Factors of 82: 1, 2, 41, 82
 Factors of 83: 1, 83
 Factors of 84: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
 Factors of 85: 1, 5, 17, 85
 Factors of 86: 1, 2, 43, 86
 Factors of 87: 1, 3, 29, 87
 Factors of 88: 1, 2, 4, 8, 11, 22, 44, 88
 Factors of 89: 1, 89
 Factors of 90: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90
 Factors of 91: 1, 7, 13, 91
 Factors of 92: 1, 2, 4, 23, 46, 92
 Factors of 93: 1, 3, 31, 93
 Factors of 94: 1, 2, 47, 94
 Factors of 95: 1, 5, 19, 95
 Factors of 96: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96
 Factors of 97: 1, 97
 Factors of 98: 1, 2, 7, 14, 49, 98
 Factors of 99: 1, 3, 9, 11, 33, 99
 Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100
 Factors of 104: 1, 2, 4, 8, 13, 26, 52, 104
 Factors of 105: 1, 3, 5, 7, 15, 21, 35, 105
 Factors of 108: 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108
 Factors of 110: 1, 2, 5, 10, 11, 22, 55, 110
 Factors of 112: 1, 2, 4, 7, 8, 14, 16, 28, 56, 112
 Factors of 117: 1, 3, 9, 13, 39, 117
 Factors of 120: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
 Factors of 121: 1, 11, 121
 Factors of 125: 1, 5, 25, 125
 Factors of 126: 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126
 Factors of 130: 1, 2, 5, 10, 13, 26, 65, 130
 Factors of 132: 1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, 132
 Factors of 135: 1, 3, 5, 9, 15, 27, 45, 135
 Factors of 140: 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, 140
 Factors of 144: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144
 Factors of 147: 1, 3, 7, 21, 49, 147
 Factors of 150: 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150
 Factors of 162: 1, 2, 3, 6, 9, 18, 27, 54, 81, 162
 Factors of 169: 1, 13, 169
 Factors of 175: 1, 5, 7, 25, 35, 175
 Factors of 180: 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180
 Factors of 189: 1, 3, 7, 9, 21, 27, 63, 189
 Factors of 192: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 192
 Factors of 196: 1, 2, 4, 7, 14, 28, 49, 98, 196
 Factors of 200: 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 200
 Factors of 210: 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210
 Factors of 216: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, 216
 Factors of 225: 1, 3, 5, 9, 15, 25, 45, 75, 225
 Factors of 240: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240
 Factors of 245: 1, 5, 7, 35, 49, 245
 Factors of 250: 1, 2, 5, 10, 25, 50, 125, 250
 Factors of 256: 1, 2, 4, 8, 16, 32, 64, 128, 256
 Factors of 270: 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 90, 135, 270
 Factors of 288: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96, 144, 288
 Factors of 294: 1, 2, 3, 6, 7, 14, 21, 42, 49, 98, 147, 294
 Factors of 300: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 300
 Factors of 343: 1, 7, 49, 343
 Factors of 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
 Factors of 375: 1, 3, 5, 15, 25, 75, 125, 375
 Factors of 400: 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400
 Factors of 500: 1, 2, 4, 5, 10, 20, 25, 50, 100, 125, 250, 500
 Factors of 625: 1, 5, 25, 125, 625
FAQ
How do I factor polynomials?
 Expand the polynomial into its prime factors. This includes the algebraic symbols as well.
 Find the factors that appear in every term, both numbers and symbols.
 Move these factors outside the brackets.
 Simplify to finally factor the polynomial.
What is prime factorization?
Prime factorization is the same as regular factorization, but where all of the factors are prime numbers. For the purposes of prime factorization, 1 is not considered a prime number.
What is a common factor?
A common factor is a factor that two numbers share. For example, 4 and 6 have a common factor of 2. Number can have multiple common factors, and finding them is an important step in finding the greatest common factor.
What are factor pairs?
Factor pairs are two numbers that, when multiplied together, result in a particular number. They are usually given as a set of factor pairs for a particular number, that is all of the pairs of numbers that, when multiplied together, equal the same number.