The document discusses two methods for determining prime numbers: the Sieve of Eratosthenes and the Sieve of Atkin. The Sieve of Eratosthenes involves listing all numbers from 1 to 100, crossing out numbers that are not prime like multiples of 2 and 3, and the remaining numbers are prime. The Sieve of Atkin is a newer and faster method that is based on the Sieve of Eratosthenes but used in algorithms due to being tedious to do by hand.

1. The Sieve of AtkinThe Sieve of Eratosthenesare methods to determine whether a given
integer is a prime number or not.
Both methods can be applied and used to create programming algorithms and the computer will
do the rest of the job for you. The Sieve of Eratosthenes is a simple way. Let say you want to find out
which numbers (from 1 to 100) are prime numbers. So, first of all you need to list all the 100 numbers
down. Then, you start crossing out numbers that are not prime numbers.
First and foremost, 1 is crossed out because it is not a prime number. Next, 2 is circled since it is the
smallest and the only even prime number. Cancel out any other even numbers because they are all
multiples of 2. This will leave you with less numbers. Next, circle 3 and cross out any other numbers that
are multiples of 3. The same routine is used and continued for the rest of the numbers until 100 and you
will all the prime numbers you need.
Meanwhile, the Sieve of Atkin is a newer and faster way. It is revised from the Sieve of Eratosthenes. The
Sieve of Atkin is used generally in an algoritm, because it is very tedious and troublesome to work out the
list manually.
Game:
Encircle all the PRIME NUNMBERS in the table.
1
11
21
31
41
51
61
71
81
91
Answer:
2
12
22
32
42
52
62
72
82
92
3
13
23
33
43
53
63
73
83
93
4
14
24
34
44
54
64
74
84
94
5
15
25
35
45
55
65
75
85
95
6
16
26
36
46
56
66
76
86
96
7
17
27
37
47
57
67
77
87
97
8
18
28
38
48
58
68
78
88
98
9
19
29
39
49
59
69
79
89
99
10
20
30
40
50
60
70
80
90
100

2. Trivia
The "Greatest Common Factor" is often abbreviated to "GCF", and is also known as:
the "Greatest Common Divisor (GCD)", or
the "Highest Common Factor (HCF)"
Answer: 4
Math Trivia #2: Least Common Multiples
The least common multiple is the smallest number that is a multiple of two numbers.
"A group of Girl Scouts goes to every 6th house to sell cookies. Another group goes to every
8th house. At which house will they first meet?"
Answer: the 24th house. It is the least common multiple of 6 and 8. (6 * 4 = 24 and 8 * 3 = 24).

3. Answer: 24