Composite Numbers from 1 to 100
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
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58
59
60
61
62
63
64
65
66
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68
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70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
Complete List of Composite Numbers (1-100)
There are 74 composite numbers between 1 and 100 (including 1 which is neither prime nor composite):
1, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100
Detailed Information for Selected Composite Numbers
| Number | Type | Factors | Special Properties | Fun Fact |
|---|---|---|---|---|
| 1 | Neither prime nor composite | 1 | Multiplicative identity | First natural number |
| 4 | Composite | 1, 2, 4 | First composite, perfect square | Seasons in a year |
| 6 | Composite | 1, 2, 3, 6 | Perfect number, factorial prime | Smallest perfect number |
| 8 | Composite | 1, 2, 4, 8 | Cube number, Fibonacci number | Number of planets in solar system |
| 9 | Composite | 1, 3, 9 | Perfect square, Motzkin number | Number of innings in baseball |
| 10 | Composite | 1, 2, 5, 10 | Triangular number, tetrahedral number | Base of decimal system |
| 12 | Composite | 1, 2, 3, 4, 6, 12 | Abundant number, highly composite | Months in a year, hours on clock |
| 16 | Composite | 1, 2, 4, 8, 16 | Perfect square, only x where x^y = y^x | Ounces in a pound |
| 24 | Composite | 1, 2, 3, 4, 6, 8, 12, 24 | Highly composite, factorial | Hours in a day |
| 36 | Composite | 1, 2, 3, 4, 6, 9, 12, 18, 36 | Square triangular number | Degrees in a circle divided by 10 |
| 49 | Composite | 1, 7, 49 | Perfect square, semiprime | Days in 7 weeks |
| 64 | Composite | 1, 2, 4, 8, 16, 32, 64 | Perfect square and cube | Squares on chessboard |
| 100 | Composite | 1, 2, 4, 5, 10, 20, 25, 50, 100 | Perfect square, sum of first 9 primes | Percentage system base |
Interesting Patterns
- The smallest composite number is 4
- All even numbers greater than 2 are composite
- The largest composite number under 100 is 100 itself
- There are 25 prime numbers and 74 composite numbers between 1-100 (including 1)
- Some composite numbers like 6, 28, and 496 are perfect numbers (equal to the sum of their proper divisors)
Composite Number Theorems
- Fundamental Theorem of Arithmetic: Every composite number can be expressed as a unique product of prime numbers
- Wilson's Theorem: A number n > 1 is composite if and only if (n-1)! ≡ 0 mod n
- Fermat's Little Theorem: If p is prime, then a^(p-1) ≡ 1 mod p for any integer a not divisible by p (used to test for compositeness)
- Primality Tests: Many algorithms exist to determine if a number is composite without finding its factors
Applications of Composite Numbers
- Mathematics: Essential in number theory and factorization problems
- Cryptography: RSA encryption relies on the difficulty of factoring large composite numbers
- Computer Science: Used in hashing algorithms and pseudorandom number generation
- Real World: Appear in measurement systems (12 inches in a foot, 60 seconds in a minute)