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 by 3.

4: A number is divisible by 4 if the last two digits form a number that is divisible by 4.

5: Any number ending in 5 or 0 is divisible by 5.

6: A number is divisible by 6 if it is divisible by 2 and 3.

8: If the last three digits form a number that is divisible by 8, then the entire number is divisible by 8.

9: If the sum of the digits is divisible by 9, the entire number is divisible by 9.

10: Any number ending in 0 is divisible by 10.

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 1Take the last digitDouble the last digitTake the remaining digitsFind the difference between the number from remaining digits and doubled last digitContinue to do this procedure until a number known to be divisible by 7 (or not) is obtained

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 order8 6 4 3 1

2. **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.

And while we are learning arithmetic, make sure to check out our distributive property calculator to know how to handle complex mathematical expressions.


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