1. The document provides examples and explanations of factoring numbers into their prime factors. It discusses finding all the factors of numbers, classifying numbers by the number of factors they have, and identifying prime and composite numbers. 2. Examples are given of finding the prime factorizations of numbers such as 1020, 585, 3135, 792, and 702 through using factor trees or listing the prime factors. 3. Homework problems are assigned asking students to find the prime factorizations of additional numbers.

1. Date: 15 July, 2023
Time: 11:30 am

2. Example 1:
Express 12 as products two whole numbers.
Try it 1:
Find the factors of 70.
->
0.1,
2, 3, 4, 5, . . .
12 =
1 x 12
=
6x2
=
3x4
70 =
1X 70
=
2 x
35
=
5 x 14
=
7
x1 The factors of 70 are 1, 2, 5, 7, 10, 14,35 and 70.

3. When a number is multiplied by a non-zero whole number, we get a multiple of the
number.
The multiples of 3 are:
Do you see the link between factors and multiples?
(cannotbe zerol
-...
2, 6, 9, 12, 15....
3 is a factor of 12.
12 is a
multiple of 3.

4. Activity
1. Copy the table below. Consider the following whole numbers, list their factors in the
table.
1.2
1.3
1, 2, 4
e n

5. 2. Classify each of the above numbers according to the number of factors they have.
Copy the table below to help you organize.
3. Observe those numbers that have only two factors. List them out. What patterns do
you observe about the factors of these numbers? The numbers that you have listed out
have a special name. Do you know what they are called?
4. Let us examine the numbers 0 and 1. How many factors do they have?
2,3,5,7-> prime
numbers -
are numbers that
are greater
than 1
and have factors of 1 and itself
4,9
6, 8, 10 ->
is the only
even number which is a
prime number
e.g. 2,3, 5, 7, 11, 13, 17, 19, 23, 29
Note:not
all odd numbers are prime
numbers
O has infinitely
many
factors e.g. 0 =
1x0 =
2x0 =
1000 x0
I has only one factor (itself) 1x1 =
1

6. C. Primes
Example 2:
Show and explain whether the following are prime or composite numbers.
(a) 851 (b) 113
e.g. 9, 15, 21,27
4, 6, 8, 9, 10, 12, 14, 15....
8 + 5+ 1 =
14 (cannot
be divided by 3):113 is a
prime number.
852
=
8 +
5 +
2 =
15
-
23x37 =
851
... 851 is a composite number

8. Example 3:
Find the prime factorisation of 1020.
Try It 3:
Find the prime factorisation of 585 using a factor tree.
10C0
N
10
10
⑧
③
:1020 =
2x2 x3 x5 x
17
eeworeno,
na probably examplee

9. Example 4:
Find the prime factorisation of 3135.
Try it 4:
Find the prime factorisation of 2730.

11. Example 5:
Find the prime factorisation of 792, expressing the answer in index notation.
Try it 5:
Find the prime factorisation of 702, expressing the answer in index notation.

12. Homework
1.

13. Homework
2.

14. Homework
3.

15. Homework
4.

16. Homework
5.