Composite Numbers

What is a Composite Number?

A whole number that can be divided evenly by numbers other than 1 or itself. In other words a composite number is a positive integer that can be formed by multiplying together two smaller positive integers. Other than number 1 every other positive number that is not a prime is a composite number.

An Example of a composite number

Every composite number can be written as the product of two or more (not necessarily distinct) primes. For example the composite number 456 can be written as 2 x 2 x 2 ,3 ,19

Types of composite numbers

One way to categorize composite numbers is to count the number of prime factors.

Semiprime - A composite number with exactly two prime factors.
Sphenic Number - A composite with three distinct prime factors
Powerful Number - When all the prime factors of a number are repeated
Squarefree - When none of the prime factors of a number are repeated

Another way to classify composite numbers is by counting the number of divisors. All composite numbers have at least three divisors.

A number n that has more divisors than any x < n is a highly composite number

Meaning of a composite number

How can you tell if a number is composite or a prime?

Find all the factors of the number
If the number has only two factors, 1 and itself, then it is prime
If the number has more than two factors, then it is composite

Recognizing prime and composite numbers

List of first 150 Composite Numbers

Sequence	Composite Number
1	4
2	6
3	8
4	9
5	10
6	12
7	14
8	15
9	16
10	18
11	20
12	21
13	22
14	24
15	25
16	26
17	27
18	28
19	30
20	32
21	33
22	34
23	35
24	36
25	38
26	39
27	40
28	42
29	44
30	45
31	46
32	48
33	49
34	50
35	51
36	52
37	54
38	55
39	56
40	57
41	58
42	60
43	62
44	63
45	64
46	65
47	66
48	68
49	69
50	70
51	72
52	74
53	75
54	76
55	77
56	78
57	80
58	81
59	82
60	84
61	85
62	86
63	87
64	88
65	90
66	91
67	92
68	93
69	94
70	95
71	96
72	98
73	99
74	100
75	102
76	104
77	105
78	106
79	108
80	110
81	111
82	112
83	114
84	115
85	116
86	117
87	118
88	119
89	120
90	121
91	122
92	123
93	124
94	125
95	126
96	128
97	129
98	130
99	132
100	133
101	134
102	135
103	136
104	138
105	140
106	141
107	142
108	143
109	144
110	145
111	146
112	147
113	148
114	150