A factor, also known as a divisor, is any number that will divide neatly into another number. They are also numbers that you multiply to get another product – but one that leaves no remainder behind.
An example of a factor is 4 x 6. Both four and six are factors.
However, defining a factor and how you explain it can depend on who you ask. Some people say that factors can be negative, but when you are using a factor calculator, you’re merely working with positive factors.
Let’s take the number 10. The factors for 10 are 1, 2, 5, and 10. However, possible factors could also be negative numbers as long as they reach 10 with no remainders. For the sake of our factor calculator, we won’t be covering negative numbers as they are not common. Instead, just know that if you put a minus in front of a value, it becomes a negative factor.
Remember when you first learned how to count to ten? It was a process and one that took a lot of practice. When you are trying to determine the rules of divisibility, the same concept applies. When you are learning to count to ten regarding rules of divisibility, here is what you need to know.
2. Any even number is divisible by 2
3. Any number, as long as the sum of the digits is divisible by 3
4. Last two digits have to form a number that’s divisible by 4
5. If the number ends in 5 or 0, it’s divisible by 5
6. If it’s divisible by 2 or 3, it’s divisible by 6
7. Believe it or not, the divisibility rule applies to 7, but you can find out more about it below
8. A number is divisible by 8 if the last three digits are divisible by it
9. A number is divisible by nine if the digit’s sum is too
10. If it ends in 0, it’s divisible by 10
This set of rules is helpful for anything relating to factors. You can also use a factor calculator to determine the least common multiple and prime factors and the greatest common factor as well.
As mentioned in the previous section, some numbers are divisible by 7, but it can be quite complicated. There are two ways you can find out.
The first method:
Take a number such as 1603 then use the following steps.
1. Identify the last digit
3
2. Double the last digit
2 x 3 = 6
3. Identify the leftover digits
160
4. Find out the difference between the doubled last digit and the remaining digits
160 – 6 = 154
5. Repeat until you know if it’s divisible.
(1603 has factors of 1, 7, 229, and 1603)
The second method:
1. Identify the digits in reverse order.
1603 becomes 3 0 6 1
2. Multiply them by the digits
3. Add them together and if it’s divisible by 7, so is your original figure
Three things might pique your curiosity in the realm of factors, and that’s prime factorization, greatest common factor, and least common multiple.
Prime factorization: this is when all the factors are prime numbers. Let’s say you had the number 24. The factors are 1, 2, 3, 4, 6, 8, 12, and 24. Not all of them are prime numbers though, so you need to break it down even further.
Greatest common factor: Equally as interesting as prime factorization is the greatest common factor – when referring to a set of numbers. Once you know the prime factorization, you can multiply all the factors in the same set. If you want to know the greatest common factor of 24, 44, and 68, you identify the prime factorizations first.
These are 2 x 2 x 2 x 3 for 24, 2 x 2 x 11 for 44, and 2 x 2 x 17 for 68. The only common factor in all of these sets is two which is in common twice with all three numbers. Therefore, the greatest common factor is 2 x 2 = 4. You can also use a Greatest Common Factor (GCF) calculator to work this out.
Least common multiple: the least common multiple (LCM) refers to the common multiple that appears the least. Identify the prime factorizations and multiply the highest power.
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
