Unit nine
Factors and Multiples
Grade seven
2024-2025
Objectives
Understandfactors, multiples, prime factors,
highest common factors and lowest common
multiples.
Understandthe hierarchy of natural
numbers, integers and rational numbers.
Warm Up
Find
1x5 2x5 3x5
Answer
1x5=5 2 x 5 = 10 3 x 5 = 15
What do we call these numbers?
5, 10, and 15 are multiples of 5
LESSON STARTER - Worksheet
LESSON STARTER - Worksheet Answers
LESSON STARTER - Worksheet Answers
Definition
A prime number is a number which has only two factors, these being
1 and the number itself.
Prime Numbers: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, …
"Factors" are the numbers we can multiply together to get
another number:
Factor Trees
Find the prime factors of 45.
45= 3x3x5= 3²x5
Highest common factors and lowest
common multiples
What are the factors of 24 and 28?
So, HCF(24, 28) = 4
Highest common factors and lowest
common multiples
What is the lowest common multiple of 24 and 28?
Multiples of 24 are: 24, 48, 72, 96, 120, 144, 168, 192, 216 …
Multiples of 28 are: 28, 56, 84, 112, 140, 168, 196, 224 …
So, LCM(24, 28) = 168
Highest common factors and lowest
common multiples using factor tree
24= x 3 28= x 7
HCF(24, 28) = =4
LCM(24, 28) = x 3 x 7 =168
General Rule
To find HCF of 2 or more numbers:
• Write the factor tree of both
• Take the common bases raised to the least power
24= x 3 28= x 7
HCF(24, 28) = =4
General Rule
To find LCM of 2 or more numbers:
• Write the factor tree of both
• Take the uncommon bases and common bases raised to the highest
power
24= x 3 28= x 7
LCM(24, 28) = x 3 x 7 =168
Please Solve Exercise 9.1 page 86
Answers
Numbers
An integer is a whole number that can be positive, negative or
zero.
Example: -3, 15, 0, ………
A natural number is an integer greater than zero.
Example: 34, 150, 20, ………
A rational number is any number that can be written as a fraction.
Example: 0.5 = , 32.456 =, ……
Any terminating decimal or recurring decimal can be written as a
fraction.
Worked exercise
Put a tick in the correct place
Please Solve Exercise 9.2 page 89
Workbook Answers
