1) The document discusses factors and multiples, including exploring arrangements of toothpicks into multiples with no leftovers. It provides examples of listing factors and multiples. 2) Prime and composite numbers are defined. A prime number has only two factors, 1 and itself, while a composite number has more than two factors. 3) The Sieve of Eratosthenes method for finding prime numbers is shown using a 100-number chart with prime numbers circled and composite numbers crossed out.

1. Factors and Multiples
Exploration : Arrange 18 toothpicks into multiples with no leftover
= 1 x 18 = 18 x 1
=2x9=9x2
=3x6=6x3
18 is the multiple of : 1, 2, 3, 6, 9, 18
1,2, 3, 6, 9 , 18 are factors of 18 18 is divisible by 1, 2, 3, 6, 9 , 18

2. Example 1
a. List the factors of 60 b. List the multiples of 5
60 = 1 x 60 = 2 x 30 = 3 x 20 5, 10, 15, 20, ….
= 4 x 15 = 5x 12 = 6 x 10
The factors of 60 are : 1, 2, 3, 4, 5, 6,
10 , 12, 15, 20 , 30, 60

3. Prime and Composite Numbers
Prime number is a number which has only 2 different factors , 1 and the
number itself
Example : 2, 3, 5, 7, 11, ….
Composite number is a number which has more than 2 different factors
Example : 4, 6, 8, 9, 10, ….
The number 1 is neither a prime number nor a composite number . Why ?
Because 1 has only 1 factor which is itself

4. Sieve of Eratosthenes
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
31 32 33 34 35 36 37 38 39 40
41 42 43 44 45 46 47 48 49 50
51 52 53 54 55 56 57 58 59 60
61 62 63 64 65 66 67 68 69 70
71 72 73 74 75 76 77 78 79 80
81 82 83 84 85 86 87 88 89 90
91 92 93 94 95 96 97 98 99 100
The circled numbers are prime numbers The red cross numbers are composite numbers
The prime numbers below than 100 : 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47,
53, 59, 61, 67, 71, 73, 79, 83, 89, 97
The number 2 is the only prime number which is even

5. Exercise 1a
1. Write down all the factors of each of the following.
a. 16 = 1 x 16 = 2 x 8 = 4 x 4 Factors of 16 are 1, 2, 4, 8, 16
b. 28 = 1 x 28 = 2 x 14 = 4 x 7 Factors of 28 are 1, 2, 4,7, 14, 28
c. 96 = 1 x 96 = 2 x 48 = 3 x 32 = 4 x 24 = 6 x 16 = 8 x 12
Factors of 97are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96
d. 100 = 1 x 100 = 2 x 50 = 4 x 25 = 5 x 5
Factors of 100 are 1, 2, 4, 5, 10, 20, 25, 100
e. 120 = 1 x 120 = 2 x 60 = 3 x 40 = 4 x 30 = 5 x 24 = 6 x 20 = 8 x 15 = 10 x 12
Factors of 120 are 1, 2, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120

6. 2. Write down the first six multiples of 4. Identify the numbers below which
the following numbers. are factor of 144
a. 4 = 4 , 8, 12, 16, 20, 24
1, 2, 3, 4, 8, 9, 12, 14, 16, 32, 48, 144
b. 7 = 7, 14, 21, 28, 35, 42
So the numbers which are factors of 144
c. 9 = 9 , 18, 27, 36, 45, 54 are : 1, 2, 3, 4, 8, 9, 12, 16, 48, and 144.
d. 12 = 12, 24, 36, 48, 60 , 72
5. Identify the multiples of 8 from the
following number
e. 17 = 17, 34, 51, 68, 85, 102
14, 24, 32, 54, 56, 36, 72, 30 , 64, 18, 40,
f. 21 = 21, 42, 63, 84, 105, 126 78, 96, 108, 120
3. Identify the numbers below that have 18 as So the numbers which are multiples of
a factor. 8 are 24, 32, 56, 72, 64, 40, 96, and 120
a. 54 : 18 = 3 So the numbers
b. 126 : 18 = 7 have 18 as a factor
c. 198 : 18 = 11 are 54, 126, 198
d. 240 : 18 = 13.33
e. 320 : 18 = 17,78

7. 6. Identify the numbers that have a. John wishes to divide his sweets equally
224 as a multiple in the following. into bags. List all the possible ways he can
do this.
224 : 3 = 74.67 48 = 1 x 48 = 2 x 24 = 3 x 16 = 4 x 12 = 6 x 8
224 : 4 = 56
224 : 12 = 18.67 So he put 2 candies into 24 bags, 3 candies into
224 : 14 = 16 16 bags, 4 candies into 12 bags, 6 candies into 8
224 : 24 = 9.33 bags, 8 candies into 6 bags, 12 candies into 4
224 : 28 =8 bags , 16 candies into 3 bags and 24 candies into
224 : 32 =7 2 bags
224 : 36 = 6.22 b. Susan also wishes to divide her sweets equally
224 : 56 =4 into bags. List all the possible ways she can do
So the numbers that have 224 this
as multiple are 4, 14, 28,32, 45 = 1 x 45 = 3 x 15 = 5 x 9
and 52
So he put 3 candies into 15 bags, 35 candies
7. John has 48 orange – into 9 bags, 9candies into 5 bags, 15 candies
flavored sweets and Susan into 3 bags
has 45 lime-flavored
sweets.

8. c. Peter, their good friend, suggests that they 11. Find the two prime numbers
combine the sweets and divide them equally into whose sum is an odd numbers
bags in such a way that each bag has equal
2+3=5
number of orange-flavored and lime-flavored
sweets. Explain how this can be done. 2+5=7
48 and 45 has common factor of 3.
So they use 3 bags each contained 16 orange-
flavored and 15 lime-flavored candies.
9. Determine whether each of the following is a
prime number or a composite number
a. 2 prime b. 15 composite
c. 17 prime d. 21 composite
e. 27 composite f. 29 prime
10. Name the next five prime numbers after 30
31, 37, 41, 43, 47