## 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.

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## 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 |