Factors of Numbers 1 to 100 (Full Table)
A factor of a number divides it exactly, leaving remainder 0. Among the integers 1 to 100, the numbers 60, 72, 84, 90 and 96 have the most factors (12 each), while every prime has exactly 2.
Total Integers100numbers 1 to 100
Most Factors (1-100)12 factorsNumbers 60, 72, 84, 90, 96
Least Factors1Number 1
Primes with 2 Factors25 numbers1 and itself
Core Formula & Rules
| Rule | What It Means | Example |
|---|---|---|
| Divisibility Definition | An integer d is a factor of n if n % d == 0 (the remainder is 0). | 12 % 4 = 0, so 4 is a factor of 12. |
| Prime Numbers | Exactly 2 factors: 1 and the number itself. | 13 has only the factors 1 and 13. |
| Square Numbers | Always have an odd number of total factors, because one factor pairs with itself. | 36 has 9 factors: 1, 2, 3, 4, 6, 9, 12, 18, 36. |
| Proper Divisors | All factors of n except n itself. Their sum is σ(n) − n. | 28: 1 + 2 + 4 + 7 + 14 = 28, a perfect number. |
Example: factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72 (12 factors, sum 195)
| Number (N) | All Factors | Total Factors d(n) | Sum of Factors σ(n) | Type | Copy |
|---|---|---|---|---|---|
| Numbers 1 to 25 | |||||
| 1 | 1 | 1 | 1 | Unit | |
| 2 | 1, 2 | 2 | 3 | Prime | |
| 3 | 1, 3 | 2 | 4 | Prime | |
| 4 | 1, 2, 4 | 3 | 7 | Square | |
| 5 | 1, 5 | 2 | 6 | Prime | |
| 6 | 1, 2, 3, 6 | 4 | 12 | Composite | |
| 7 | 1, 7 | 2 | 8 | Prime | |
| 8 | 1, 2, 4, 8 | 4 | 15 | Composite | |
| 9 | 1, 3, 9 | 3 | 13 | Square | |
| 10 | 1, 2, 5, 10 | 4 | 18 | Composite | |
| 11 | 1, 11 | 2 | 12 | Prime | |
| 12 | 1, 2, 3, 4, 6, 12 | 6 | 28 | Composite | |
| 13 | 1, 13 | 2 | 14 | Prime | |
| 14 | 1, 2, 7, 14 | 4 | 24 | Composite | |
| 15 | 1, 3, 5, 15 | 4 | 24 | Composite | |
| 16 | 1, 2, 4, 8, 16 | 5 | 31 | Square | |
| 17 | 1, 17 | 2 | 18 | Prime | |
| 18 | 1, 2, 3, 6, 9, 18 | 6 | 39 | Composite | |
| 19 | 1, 19 | 2 | 20 | Prime | |
| 20 | 1, 2, 4, 5, 10, 20 | 6 | 42 | Composite | |
| 21 | 1, 3, 7, 21 | 4 | 32 | Composite | |
| 22 | 1, 2, 11, 22 | 4 | 36 | Composite | |
| 23 | 1, 23 | 2 | 24 | Prime | |
| 24 | 1, 2, 3, 4, 6, 8, 12, 24 | 8 | 60 | Composite | |
| 25 | 1, 5, 25 | 3 | 31 | Square | |
| Numbers 26 to 50 | |||||
| 26 | 1, 2, 13, 26 | 4 | 42 | Composite | |
| 27 | 1, 3, 9, 27 | 4 | 40 | Composite | |
| 28 | 1, 2, 4, 7, 14, 28 | 6 | 56 | Composite | |
| 29 | 1, 29 | 2 | 30 | Prime | |
| 30 | 1, 2, 3, 5, 6, 10, 15, 30 | 8 | 72 | Composite | |
| 31 | 1, 31 | 2 | 32 | Prime | |
| 32 | 1, 2, 4, 8, 16, 32 | 6 | 63 | Composite | |
| 33 | 1, 3, 11, 33 | 4 | 48 | Composite | |
| 34 | 1, 2, 17, 34 | 4 | 54 | Composite | |
| 35 | 1, 5, 7, 35 | 4 | 48 | Composite | |
| 36 | 1, 2, 3, 4, 6, 9, 12, 18, 36 | 9 | 91 | Square | |
| 37 | 1, 37 | 2 | 38 | Prime | |
| 38 | 1, 2, 19, 38 | 4 | 60 | Composite | |
| 39 | 1, 3, 13, 39 | 4 | 56 | Composite | |
| 40 | 1, 2, 4, 5, 8, 10, 20, 40 | 8 | 90 | Composite | |
| 41 | 1, 41 | 2 | 42 | Prime | |
| 42 | 1, 2, 3, 6, 7, 14, 21, 42 | 8 | 96 | Composite | |
| 43 | 1, 43 | 2 | 44 | Prime | |
| 44 | 1, 2, 4, 11, 22, 44 | 6 | 84 | Composite | |
| 45 | 1, 3, 5, 9, 15, 45 | 6 | 78 | Composite | |
| 46 | 1, 2, 23, 46 | 4 | 72 | Composite | |
| 47 | 1, 47 | 2 | 48 | Prime | |
| 48 | 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 | 10 | 124 | Composite | |
| 49 | 1, 7, 49 | 3 | 57 | Square | |
| 50 | 1, 2, 5, 10, 25, 50 | 6 | 93 | Composite | |
| Numbers 51 to 75 | |||||
| 51 | 1, 3, 17, 51 | 4 | 72 | Composite | |
| 52 | 1, 2, 4, 13, 26, 52 | 6 | 98 | Composite | |
| 53 | 1, 53 | 2 | 54 | Prime | |
| 54 | 1, 2, 3, 6, 9, 18, 27, 54 | 8 | 120 | Composite | |
| 55 | 1, 5, 11, 55 | 4 | 72 | Composite | |
| 56 | 1, 2, 4, 7, 8, 14, 28, 56 | 8 | 120 | Composite | |
| 57 | 1, 3, 19, 57 | 4 | 80 | Composite | |
| 58 | 1, 2, 29, 58 | 4 | 90 | Composite | |
| 59 | 1, 59 | 2 | 60 | Prime | |
| 60 | 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 | 12 | 168 | Composite | |
| 61 | 1, 61 | 2 | 62 | Prime | |
| 62 | 1, 2, 31, 62 | 4 | 96 | Composite | |
| 63 | 1, 3, 7, 9, 21, 63 | 6 | 104 | Composite | |
| 64 | 1, 2, 4, 8, 16, 32, 64 | 7 | 127 | Square | |
| 65 | 1, 5, 13, 65 | 4 | 84 | Composite | |
| 66 | 1, 2, 3, 6, 11, 22, 33, 66 | 8 | 144 | Composite | |
| 67 | 1, 67 | 2 | 68 | Prime | |
| 68 | 1, 2, 4, 17, 34, 68 | 6 | 126 | Composite | |
| 69 | 1, 3, 23, 69 | 4 | 96 | Composite | |
| 70 | 1, 2, 5, 7, 10, 14, 35, 70 | 8 | 144 | Composite | |
| 71 | 1, 71 | 2 | 72 | Prime | |
| 72 | 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72 | 12 | 195 | Composite | |
| 73 | 1, 73 | 2 | 74 | Prime | |
| 74 | 1, 2, 37, 74 | 4 | 114 | Composite | |
| 75 | 1, 3, 5, 15, 25, 75 | 6 | 124 | Composite | |
| Numbers 76 to 100 | |||||
| 76 | 1, 2, 4, 19, 38, 76 | 6 | 140 | Composite | |
| 77 | 1, 7, 11, 77 | 4 | 96 | Composite | |
| 78 | 1, 2, 3, 6, 13, 26, 39, 78 | 8 | 168 | Composite | |
| 79 | 1, 79 | 2 | 80 | Prime | |
| 80 | 1, 2, 4, 5, 8, 10, 16, 20, 40, 80 | 10 | 186 | Composite | |
| 81 | 1, 3, 9, 27, 81 | 5 | 121 | Square | |
| 82 | 1, 2, 41, 82 | 4 | 126 | Composite | |
| 83 | 1, 83 | 2 | 84 | Prime | |
| 84 | 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84 | 12 | 224 | Composite | |
| 85 | 1, 5, 17, 85 | 4 | 108 | Composite | |
| 86 | 1, 2, 43, 86 | 4 | 132 | Composite | |
| 87 | 1, 3, 29, 87 | 4 | 120 | Composite | |
| 88 | 1, 2, 4, 8, 11, 22, 44, 88 | 8 | 180 | Composite | |
| 89 | 1, 89 | 2 | 90 | Prime | |
| 90 | 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90 | 12 | 234 | Composite | |
| 91 | 1, 7, 13, 91 | 4 | 112 | Composite | |
| 92 | 1, 2, 4, 23, 46, 92 | 6 | 168 | Composite | |
| 93 | 1, 3, 31, 93 | 4 | 128 | Composite | |
| 94 | 1, 2, 47, 94 | 4 | 144 | Composite | |
| 95 | 1, 5, 19, 95 | 4 | 120 | Composite | |
| 96 | 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96 | 12 | 252 | Composite | |
| 97 | 1, 97 | 2 | 98 | Prime | |
| 98 | 1, 2, 7, 14, 49, 98 | 6 | 171 | Composite | |
| 99 | 1, 3, 9, 11, 33, 99 | 6 | 156 | Composite | |
| 100 | 1, 2, 4, 5, 10, 20, 25, 50, 100 | 9 | 217 | Square | |
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Frequently Asked Questions
| Question | Answer |
|---|---|
| What are the factors of a number? | The factors of a number are the integers that divide it exactly, with remainder 0. For example, the factors of 12 are 1, 2, 3, 4, 6 and 12. |
| Which numbers from 1 to 100 have the most factors? | The numbers 60, 72, 84, 90 and 96 each have 12 factors, the most of any number from 1 to 100. |
| How many factors does a prime number have? | A prime number has exactly 2 factors: 1 and itself. There are 25 prime numbers from 1 to 100. |
| Why do square numbers have an odd number of factors? | Factors come in pairs (d, n/d). In a square number the square root pairs with itself and is counted only once, so the total is odd. For example, 36 has 9 factors. |
| What are the factors of 100? | The factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, 100, which is 9 factors in total. |
| What is the difference between factors and proper divisors? | Proper divisors are all the factors of a number except the number itself. The proper divisors of 12 are 1, 2, 3, 4 and 6. |
Related Number Theory References
| Related Page | What You Will Find |
|---|---|
| Prime Factorization Table (1-100) | Prime factors and exponential form for every number from 1 to 100. |
| Prime Numbers (1-1000) | All 168 primes up to 1000 with a prime checker and distribution table. |
| Co-Prime Numbers (1-100) | Co-prime rules, a pairs chart and a two-number co-prime tester. |
| Twin Primes up to 1000 | All 35 twin prime pairs with an instant pair checker. |