# 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

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

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

## Recognizing prime and composite numbers

### List of first 150 Composite Numbers

SequenceComposite Number
14
26
38
49
510
612
714
815
916
1018
1120
1221
1322
1424
1525
1626
1727
1828
1930
2032
2133
2234
2335
2436
2538
2639
2740
2842
2944
3045
3146
3248
3349
3450
3551
3652
3754
3855
3956
4057
4158
4260
4362
4463
4564
4665
4766
4868
4969
5070
5172
5274
5375
5476
5577
5678
5780
5881
5982
6084
6185
6286
6387
6488
6590
6691
6792
6893
6994
7095
7196
7298
7399
74100
75102
76104
77105
78106
79108
80110
81111
82112
83114
84115
85116
86117
87118
88119
89120
90121
91122
92123
93124
94125
95126
96128
97129
98130
99132
100133
101134
102135
103136
104138
105140
106141
107142
108143
109144
110145
111146
112147
113148
114150