Prime factorization of a composite number is expressing the number as a product of prime numbers. The prime factorization is useful in determining the Greatest common factor and hence the Lowest common multiple of a number.There is only one prime factorization for any number as the order of factors does not matter.

## Methods of finding prime factorization

- Checking divisibility repeatedly
- Using a factor tree.

## What is a prime factorization chart?

## Prime factorization chart 1-100

It is good idea to list out the prime numbers in the list 1 to 100

Note 1 is neither a prime nor a composite number as it has only one factor that is itself. The prime numbers from 1 to 100 are,

2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83, 89 and 97.

In the table these numbers can be stated as prime.

The prime factorization for other numbers can be done from starting from the smallest composite number 4.

If a larger number has a smaller composite factors, the prime factors of the smaller can be used. It would not be necessary to find the prime factors of all composite numbers.

For example 8 = 2 x 4. The prime factors of 4 = 2 x 2. Hence the prime factorization of 8 = 2 x 2 x 2. The table can be thus completed till 100.

Number |
Prime Factorization |
Number |
Prime Factorization |

1 | Not composite | 11 | Prime |

2 | Prime | 12 | 2 x 2 x 3 |

3 | Prime | 13 | Prime |

4 | 2 x 2 | 14 | 2 x 7 |

5 | Prime | 15 | 3 x 5 |

6 | 2 x 3 | 16 | 2 x 2 x 2 x 2 |

7 | Prime | 17 | Prime |

8 | 2 x 2 x 2 | 18 | 2 x 3 x 3 |

9 | 3 x 3 |
19 | Prime |

10 | 2 x 5 | 20 | 2 x 2 x 5 |

Number |
Prime Factorization |
Number |
Prime Factorization |

21 | 3 x 7 | 31 | Prime |

22 | 2 x 11 | 32 | 2 x 2 x 2 x 2 x 2 |

23 | Prime | 33 | 3 x 11 |

24 | 2 x 2 x 2 x 3 | 34 | 2 x 17 |

25 | 5 x 5 | 35 | 5 x 7 |

26 | 2 x 13 | 36 | 2 x 2 x 3 x 3 |

27 | 3 x 3 x 3 | 37 | Prime |

28 | 2 x 2 x 7 | 38 | 2 x 19 |

29 | Prime | 39 | 3 x 13 |

30 | 2 x 3 x 5 | 40 | 2 x 2 x 2 x 5 |

Number |
Prime Factorization |
Number |
Prime Factorization |

41 | Prime | 51 | 3 x 17 |

42 | 2 x 3 x 7 | 52 | 2 x 2 x 13 |

43 | Prime | 53 | Prime |

44 | 2 x 2 x 11 | 54 | 2 x 3 x 3 x 3 |

45 | 3 x 3 x 5 | 55 | 5 x 11 |

46 | 2 x 23 | 56 | 2 x 2 x 2 x 7 |

47 | Prime | 57 | 3 x 19 |

48 | 2 x 2 x 2 x 2 x 3 | 58 | 2 x 29 |

49 | 7 x 7 | 59 | Prime |

50 | 2 x 5 x 5 | 60 | 2 x 2 x 3 x 5 |

Number |
Prime Factorization |
Number |
Prime Factorization |

61 | Prime | 71 | Prime |

62 | 2 x 31 | 72 | 2 x 2 x 2 x 3 x 3 |

63 | 3 x 3 x 7 | 73 | Prime |

64 | 2 x 2 x 2 x 2 x 2 x 2 | 74 | 2 x 37 |

65 | 5 x 13 | 75 | 3 x 5 x 5 |

66 | 2 x 3 x 11 | 76 | 2 x 2 x 19 |

67 | Prime | 77 | 7 x 11 |

68 | 2 x 2 x 17 | 78 | 2 x 3 x 13 |

69 | 3 x 23 | 79 | Prime |

70 | 2 x 5 x 7 | 80 | 2 x 2 x 2 x 2 x 5 |

Number |
Prime Factorization |
Number |
Prime Factorization |

81 | 3 x 3 x 3 x 3 |
91 | 7 x 13 |

82 | 2 x 41 | 92 | 2 x 2 x 23 |

83 | Prime | 93 | 3 x 31 |

84 | 2 x 2 x 3 x 7 | 94 | 2 x 47 |

85 | 5 x 17 | 95 | 5 x 19 |

86 | 2 x 43 | 96 | 2 x 2 x 2 x 2 x 2 x 3 |

87 | 3 x 29 | 97 | Prime |

88 | 2 x 2 x 2 x 11 | 98 | 2 x 7 x 7 |

89 | Prime | 99 | 3 x 3 x 11 |

90 | 2 x 3 x 3 x 5 | 100 | 2 x 2 x 5 x 5 |