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 |