Prime Factorization 1 to 100 (Full Table)
Prime factorization breaks each composite number from 1 to 100 into a product of primes. Of these 100 numbers, 25 are prime, 74 are composite, and 1 is neither. For example, 72 = 2³ × 3².
100Total Numbers
25Prime Numbers
74Composite
1Unit (Neither)
Example: 72 = 2 × 2 × 2 × 3 × 3 = 2³ × 3²
| Number (N) | Prime Factors Breakdown | Exponential Form | Type | Copy |
|---|---|---|---|---|
| Numbers 1 to 25 | ||||
| 1 | None | — | Neither | |
| 2 | 2 | 2 | Prime | |
| 3 | 3 | 3 | Prime | |
| 4 | 2 × 2 | 2² | Composite | |
| 5 | 5 | 5 | Prime | |
| 6 | 2 × 3 | 2 × 3 | Composite | |
| 7 | 7 | 7 | Prime | |
| 8 | 2 × 2 × 2 | 2³ | Composite | |
| 9 | 3 × 3 | 3² | Composite | |
| 10 | 2 × 5 | 2 × 5 | Composite | |
| 11 | 11 | 11 | Prime | |
| 12 | 2 × 2 × 3 | 2² × 3 | Composite | |
| 13 | 13 | 13 | Prime | |
| 14 | 2 × 7 | 2 × 7 | Composite | |
| 15 | 3 × 5 | 3 × 5 | Composite | |
| 16 | 2 × 2 × 2 × 2 | 2⁴ | Composite | |
| 17 | 17 | 17 | Prime | |
| 18 | 2 × 3 × 3 | 2 × 3² | Composite | |
| 19 | 19 | 19 | Prime | |
| 20 | 2 × 2 × 5 | 2² × 5 | Composite | |
| 21 | 3 × 7 | 3 × 7 | Composite | |
| 22 | 2 × 11 | 2 × 11 | Composite | |
| 23 | 23 | 23 | Prime | |
| 24 | 2 × 2 × 2 × 3 | 2³ × 3 | Composite | |
| 25 | 5 × 5 | 5² | Composite | |
| Numbers 26 to 50 | ||||
| 26 | 2 × 13 | 2 × 13 | Composite | |
| 27 | 3 × 3 × 3 | 3³ | Composite | |
| 28 | 2 × 2 × 7 | 2² × 7 | Composite | |
| 29 | 29 | 29 | Prime | |
| 30 | 2 × 3 × 5 | 2 × 3 × 5 | Composite | |
| 31 | 31 | 31 | Prime | |
| 32 | 2 × 2 × 2 × 2 × 2 | 2⁵ | Composite | |
| 33 | 3 × 11 | 3 × 11 | Composite | |
| 34 | 2 × 17 | 2 × 17 | Composite | |
| 35 | 5 × 7 | 5 × 7 | Composite | |
| 36 | 2 × 2 × 3 × 3 | 2² × 3² | Composite | |
| 37 | 37 | 37 | Prime | |
| 38 | 2 × 19 | 2 × 19 | Composite | |
| 39 | 3 × 13 | 3 × 13 | Composite | |
| 40 | 2 × 2 × 2 × 5 | 2³ × 5 | Composite | |
| 41 | 41 | 41 | Prime | |
| 42 | 2 × 3 × 7 | 2 × 3 × 7 | Composite | |
| 43 | 43 | 43 | Prime | |
| 44 | 2 × 2 × 11 | 2² × 11 | Composite | |
| 45 | 3 × 3 × 5 | 3² × 5 | Composite | |
| 46 | 2 × 23 | 2 × 23 | Composite | |
| 47 | 47 | 47 | Prime | |
| 48 | 2 × 2 × 2 × 2 × 3 | 2⁴ × 3 | Composite | |
| 49 | 7 × 7 | 7² | Composite | |
| 50 | 2 × 5 × 5 | 2 × 5² | Composite | |
| Numbers 51 to 75 | ||||
| 51 | 3 × 17 | 3 × 17 | Composite | |
| 52 | 2 × 2 × 13 | 2² × 13 | Composite | |
| 53 | 53 | 53 | Prime | |
| 54 | 2 × 3 × 3 × 3 | 2 × 3³ | Composite | |
| 55 | 5 × 11 | 5 × 11 | Composite | |
| 56 | 2 × 2 × 2 × 7 | 2³ × 7 | Composite | |
| 57 | 3 × 19 | 3 × 19 | Composite | |
| 58 | 2 × 29 | 2 × 29 | Composite | |
| 59 | 59 | 59 | Prime | |
| 60 | 2 × 2 × 3 × 5 | 2² × 3 × 5 | Composite | |
| 61 | 61 | 61 | Prime | |
| 62 | 2 × 31 | 2 × 31 | Composite | |
| 63 | 3 × 3 × 7 | 3² × 7 | Composite | |
| 64 | 2 × 2 × 2 × 2 × 2 × 2 | 2⁶ | Composite | |
| 65 | 5 × 13 | 5 × 13 | Composite | |
| 66 | 2 × 3 × 11 | 2 × 3 × 11 | Composite | |
| 67 | 67 | 67 | Prime | |
| 68 | 2 × 2 × 17 | 2² × 17 | Composite | |
| 69 | 3 × 23 | 3 × 23 | Composite | |
| 70 | 2 × 5 × 7 | 2 × 5 × 7 | Composite | |
| 71 | 71 | 71 | Prime | |
| 72 | 2 × 2 × 2 × 3 × 3 | 2³ × 3² | Composite | |
| 73 | 73 | 73 | Prime | |
| 74 | 2 × 37 | 2 × 37 | Composite | |
| 75 | 3 × 5 × 5 | 3 × 5² | Composite | |
| Numbers 76 to 100 | ||||
| 76 | 2 × 2 × 19 | 2² × 19 | Composite | |
| 77 | 7 × 11 | 7 × 11 | Composite | |
| 78 | 2 × 3 × 13 | 2 × 3 × 13 | Composite | |
| 79 | 79 | 79 | Prime | |
| 80 | 2 × 2 × 2 × 2 × 5 | 2⁴ × 5 | Composite | |
| 81 | 3 × 3 × 3 × 3 | 3⁴ | Composite | |
| 82 | 2 × 41 | 2 × 41 | Composite | |
| 83 | 83 | 83 | Prime | |
| 84 | 2 × 2 × 3 × 7 | 2² × 3 × 7 | Composite | |
| 85 | 5 × 17 | 5 × 17 | Composite | |
| 86 | 2 × 43 | 2 × 43 | Composite | |
| 87 | 3 × 29 | 3 × 29 | Composite | |
| 88 | 2 × 2 × 2 × 11 | 2³ × 11 | Composite | |
| 89 | 89 | 89 | Prime | |
| 90 | 2 × 3 × 3 × 5 | 2 × 3² × 5 | Composite | |
| 91 | 7 × 13 | 7 × 13 | Composite | |
| 92 | 2 × 2 × 23 | 2² × 23 | Composite | |
| 93 | 3 × 31 | 3 × 31 | Composite | |
| 94 | 2 × 47 | 2 × 47 | Composite | |
| 95 | 5 × 19 | 5 × 19 | Composite | |
| 96 | 2 × 2 × 2 × 2 × 2 × 3 | 2⁵ × 3 | Composite | |
| 97 | 97 | 97 | Prime | |
| 98 | 2 × 7 × 7 | 2 × 7² | Composite | |
| 99 | 3 × 3 × 11 | 3² × 11 | Composite | |
| 100 | 2 × 2 × 5 × 5 | 2² × 5² | Composite | |
Frequently Asked Questions
| Question | Answer |
|---|---|
| What is prime factorization? | Prime factorization is writing a number as a product of prime numbers, for example 72 = 2 × 2 × 2 × 3 × 3 = 2³ × 3². |
| What is the prime factorization of 100? | The prime factorization of 100 is 2 × 2 × 5 × 5, written as 2² × 5² in exponential form. |
| Is 1 a prime or composite number? | 1 is neither prime nor composite, so it has no prime factors. |
| How many prime numbers are there between 1 and 100? | There are 25 prime numbers between 1 and 100. |
| How many composite numbers are there from 1 to 100? | There are 74 composite numbers from 1 to 100, which is every number except 1 and the 25 primes. |
| Which numbers from 1 to 100 have the most prime factors? | 64 (2⁶) and 96 (2⁵ × 3) each have 6 prime factors when repeated factors are counted. |
Related Number Theory References
| Related Page | What You Will Find |
|---|---|
| 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. |