This document discusses factors and multiples of numbers. It defines factors as numbers that can be multiplied together to get another number, and multiples as numbers obtained by multiplying a given number by whole numbers. Examples are provided to illustrate factors, multiples, and types of numbers including abundant, deficient, and perfect numbers. Practice problems are included to identify factors and multiples, as well as grouping students into equal numbers of groups.

1. Factors and Multiples
of a Number

2. At the end of this lesson, the learner should be able to
● accurately find all the factors and multiples of a
given number;
● correctly write a given number as a product of its
factors; and
● correctly solve problems involving factors and
multiples of a number.

3. ● How can you determine the factors and multiples of a
given number?
● How can you write a given number as a product of its
factors?

4. Before we start our discussion on factors and multiples, let us
see if you have mastered your multiplication skills.
(Click on the link to access the exercise.)
“Tug Team Multiplication”. Math Playground. Retrieved 13
March 2019 from http://bit.ly/2TCMl6D

5. ● Did you defeat the computer in the tug-team
multiplication? How did you come up with the product of
the two given numbers?
● What are the different strategies that you can share about
getting the product of two numbers?
● What if the given number is already a product, can you still
give two possible numbers that can be multiplied to get
the given number as result?

6. Factors
whole numbers used to multiply together to get another number; numbers that
can divide a given number equally
1
Example:

7. 2 Multiples
numbers obtained by multiplying the given number by whole numbers.
Example:
Multiples of 4: 4, 8, 12, 16, 20, 24…
𝟏 × 𝟒 = 𝟒
𝟐 × 𝟒 = 𝟖
𝟑 × 𝟒 = 𝟏𝟐
𝟒 × 𝟒 = 𝟏𝟔
𝟓 × 𝟒 = 𝟐𝟎
𝟔 × 𝟒 = 𝟐𝟒
…

8. 3
Abundant number
numbers whose sum of all its factors (excluding itself) is greater than the number
itself
Example:
Factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18 and 36.
1 × 36 = 36
2 × 18 = 36
3 × 12 = 36
4 × 9 = 36
6 × 6 = 36

9. 3
Abundant number
numbers whose sum of all its factors (excluding itself) is greater than the number
itself
Example:
Factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18 and 36.
The sum of the factors except 36 is given by:
1 + 2 + 3 + 4 + 6 + 9 + 12 + 18 = 55 > 36
Thus, 36 is an abundant number.

10. 4 Deficient numbers
numbers whose sum of all its factors (excluding itself) is less than the number itself
Example:
Factors of 21 are 1, 3, 7 and 21.
1 × 21 = 21
3 × 7 = 21

11. 4 Deficient numbers
numbers whose sum of all its factors (excluding itself) is less than the number itself
Example:
Factors of 21 are 1, 3, 7 and 21.
The sum of the factors except 21 is 11.
1 + 3 + 7 = 11 < 21
Thus, 21 is a deficient number.

12. 5 Perfect numbers
numbers whose sum of all its factors (excluding itself) is equal to the number itself
Example:
Factors of 28 are 1, 2, 4, 7, 14 and 28.
1 × 28 = 28
2 × 14 = 28
4 × 7 = 28

13. 5 Perfect numbers
numbers whose sum of all its factors (excluding itself) is equal to the number itself
Example:
Factors of 28 are 1, 2, 4, 7, 14 and 28.
The sum of the factors except 28 is 28.
1 + 2 + 4 + 7 + 14 = 28
Therefore, 28 is a perfect number.

14. Example 1: Find all the factors of 26.

15. Example 1: Find all the factors of 26.
Solution:
List down all possible pairs that when multiplied together will
give a product of 26.
Since all numbers are divisible by 1, then the first pair is:
1 × 26 = 26

16. Example 1: Find all the factors of 26.
Solution:
List down all possible pairs that when multiplied together will
give a product of 26.
If the number is even, then we can say that one of its factors
is 2. Thus, the next pair is:
2 × 13 = 26

17. Example 1: Find all the factors of 26.
Solution:
List down all possible pairs that when multiplied together will
give a product of 26.
As we increase one of the factors, the other factors tend to
decrease. Then, check if there is a number between 2 and 13
that can divide 26 equally.

18. Example 1: Find all the factors of 26.
Solution:
As we increase one of the factors, the other factors tends to
decrease. Then, check if there is a number between 2 and 13
that can divide 26 equally.
Since there are no numbers between 2 and 13 that can
divide 26 equally, the list is already completed.

19. Example 1: Find all the factors of 26.
Solution:
List down all possible pairs that when multiplied together will
give a product of 26.
Summarize the list of factors.
1 × 26 = 26
2 × 13 = 26
Thus, the factors of 26 are 1, 2, 13 and 26

20. Example 2: Find the first five multiples of 3.

21. Example 2: Find the first five multiples of 3.
Solution:
List down the first five whole numbers to be multiplied by 3.
1 × 3 = 3
2 × 3 = 6
3 × 3 = 9
4 × 3 = 12
5 × 3 = 15
Therefore, the first five multiples of 3 are 3, 6, 9, 12 and 15.

22. Individual Practice:
1. What is the smallest and the largest factors of any
number?
2. Which of the following numbers are abundant, deficient
and perfect: 16, 13, 6 ?

23. Group Practice: To be done in groups of 4.
Mr. Lopez has an activity for his Science class. He has 48
students in his class and he wants to have not less than 4
members but not more than 10 members per group. In how
many ways can he group the class with equal number of
members?

24. Factors
whole numbers used to multiply together to get another number; numbers that
can divide a given number equally
1
2
3
Multiples
numbers obtained by multiplying the given number by whole numbers.
3 Abundant Numbers
numbers whose sum of all its factors (excluding itself) is greater than the number
itself

25. Deficient Numbers
numbers whose sum of all its factors (excluding itself) is less than the number
itself
4
5 Perfect Numbers
numbers whose sum of all its factors (excluding itself) is equal to the number
itself.

26. ● How do you determine the factors and multiples of a given
number?
● Why do we need to learn about identifying the factors and
multiples of a number?
● Now that you have learned how to identify factors and
multiples of a number, are you ready to use them in
finding prime and composite numbers?