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Number

The factor calculator will determine the factors of any positive integer. A factor is any number that divides evenly into another number. There are rules of divisibility that greatly assists one in finding factors by hand. They are as follows:

- Any even number is divisible by
`2`

. - A number is divisible by
`3`

if the sum of the digits in the number is divisible by`3`

. - A number is divisible by
`4`

if the last two digits form a number that is divisible by`4`

. - Any number ending in
`5`

or`0`

is divisible by`5`

. - A number is divisible by
`6`

if it is divisible by`2`

and`3`

. - If the last three digits form a number that is divisible by
`8`

, then the entire number is divisible by`8`

. - If the sum of the digits are divisible by
`9`

, the entire number is divisible by`9`

. - Any number ending in
`0`

is divisible by`10`

.

There are many aspects of mathematics where it is important to be able to get factors. The factor calculator is helpful in finding the greatest common factor, least common multiple and prime factorization.

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 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 LCM or least common multiple. The process is nearly the same to find the LCM. We get the prime factorizations and now multiply the highest power of all factors present. IN the above example, the LCM would be `2 * 2 * 2 * 3 * 11 * 17 = 4,488`

. The use of the least common multiple calculator will make a sometimes tedious process by hand much easier.

**Note that the factor calculator gives the factors of 0 or any negative number as 1. We should only use positive integers in the factor calculator.**

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 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 105: 1, 3, 5, 7, 15, 21, 35, 105
- Factors of 117: 1, 3, 9, 13, 39, 117
- Factors of 121: 1, 11, 121
- Factors of 126: 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126
- Factors of 132: 1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, 132