# Question :- What is a Prime Number?

Answer:- These are whole numbers that are only divisible by 1 and by the number itself.

e.g. 11 = Divisible by 1 & 11

e.g. 31 = Divisible by 1 & 31

Non-prime numbers can be divided by two or more numbers.

e.g. 9 = Divisible by 1, 3 & 9

## Prime Factors

This is prime numbers that are multiplied together give arrive at the number being considered.

e.g. The prime factors of 171 are 3, 3, 19

So 171 = 3 x 3 x 19

## To find the Prime Factors of an odd number like 171

1) Look up the prime factor in the table below for 171 which is 3.

2) Divide 171 by 3 to give 57.

3) Look up 57 in the table below the smallest factor is 3 again.

4) Divide 57 by 3 to give 19.

5) Look up 19 in the table below the smallest factor is a P which means its a prime number itself.

## To find the Prime Factors of an even number like 60

1) The smallest prime factor for an even is 2.

2) Divide 60 by 2 to give 30.

3) Divide 30 by 2 to give 15.

4) Look up 15 in the table below the smallest factor is 3 again.

5) Divide 15 by 3 to give 3.

6) Look up 3 in the table below the smallest factor is a P which means its a prime number itself.

## Odd Prime Numbers & smallest factor lookup table

000s | 100s | 200s | 300s | 400s | 500s | 600s | 700s | 800s | 900s | |
---|---|---|---|---|---|---|---|---|---|---|

1 | P | P | 3 | 7 | P | 3 | P | P | 3 | 17 |

3 | P | P | 7 | 3 | 13 | P | 3 | 19 | 11 | 3 |

5 | P | 3 | 5 | 5 | 3 | 5 | 5 | 3 | 5 | 5 |

7 | P | P | 3 | P | 11 | 3 | P | 7 | 3 | P |

11 | P | 3 | P | P | 3 | 7 | 13 | 3 | P | P |

13 | P | P | 3 | P | 7 | 3 | P | 23 | 3 | 11 |

15 | 3 | 5 | 5 | 3 | 5 | 5 | 3 | 5 | 5 | 3 |

17 | P | 3 | 7 | P | 3 | 11 | P | 3 | 19 | 7 |

19 | P | 7 | 3 | 11 | P | 3 | P | P | 3 | P |

21 | 3 | 11 | 13 | 3 | P | P | 3 | 7 | P | 3 |

23 | P | 3 | P | 17 | 3 | P | 7 | 3 | P | 13 |

25 | 5 | 5 | 3 | 5 | 5 | 3 | 5 | 5 | 3 | 5 |

27 | 3 | P | P | 3 | 7 | 17 | 3 | P | P | 3 |

29 | P | 3 | P | 7 | 3 | 23 | 17 | 3 | P | P |

31 | P | P | 3 | P | P | 3 | P | 17 | 3 | 7 |

33 | 3 | 7 | P | 3 | P | 13 | 3 | P | 7 | 3 |

35 | 5 | 3 | 5 | 5 | 3 | 5 | 5 | 3 | 5 | 5 |

37 | P | P | 3 | P | 19 | 3 | 7 | 11 | 3 | P |

39 | 3 | P | P | 3 | P | 7 | 3 | P | P | 3 |

41 | P | 3 | P | 11 | 3 | P | P | 3 | 29 | P |

43 | P | 11 | 3 | 7 | P | 3 | P | P | 3 | 23 |

45 | 3 | 5 | 5 | 3 | 5 | 5 | 3 | 5 | 5 | 3 |

47 | P | 3 | 13 | P | 3 | P | P | 3 | 7 | P |

49 | 7 | P | 3 | P | P | 3 | 11 | 7 | 3 | 13 |

51 | 3 | P | P | 3 | 11 | 19 | 3 | P | 23 | 3 |

53 | P | 3 | 11 | P | 3 | 7 | P | 3 | P | P |

55 | 5 | 5 | 3 | 5 | 5 | 3 | 5 | 5 | 3 | 5 |

57 | 3 | P | P | 3 | P | P | 3 | P | P | 3 |

59 | P | 3 | 7 | P | 3 | 13 | P | 3 | P | 7 |

61 | P | 7 | 3 | 19 | P | 3 | P | P | 3 | 31 |

63 | 3 | P | P | 3 | P | P | 3 | 7 | P | 3 |

65 | 5 | 3 | 5 | 5 | 3 | 5 | 5 | 3 | 5 | 5 |

67 | P | P | 3 | P | P | 3 | 23 | 13 | 3 | P |

69 | 3 | 13 | P | 3 | 7 | P | 3 | P | 11 | 3 |

71 | P | 3 | P | 7 | 3 | P | 11 | 3 | 13 | P |

73 | P | P | 3 | P | 11 | 3 | P | P | 3 | 7 |

75 | 3 | 5 | 5 | 3 | 5 | 5 | 3 | 5 | 5 | 3 |

77 | 7 | 3 | P | 13 | 3 | P | P | 3 | P | P |

79 | P | P | 3 | P | P | 3 | 7 | 19 | 3 | 11 |

81 | 3 | P | P | 3 | 13 | 7 | 3 | 11 | P | 3 |

83 | P | 3 | P | P | 3 | 11 | P | 3 | P | P |

85 | 5 | 5 | 3 | 5 | 5 | 3 | 5 | 5 | 3 | 5 |

87 | P | 3 | 11 | 7 | 3 | P | P | 3 | P | P |

89 | P | 3 | 17 | P | 3 | 19 | 13 | 3 | 7 | 23 |

91 | 7 | P | 3 | 17 | P | 3 | P | 7 | 3 | P |

93 | 3 | P | P | 3 | 17 | P | 3 | 13 | 19 | 3 |

95 | 5 | 3 | 5 | 5 | 3 | 5 | 5 | 3 | 5 | 5 |

97 | P | P | 3 | P | 7 | 3 | 17 | P | 3 | P |

99 | 3 | P | 13 | 3 | P | P | 3 | 17 | 29 | 3 |