This document discusses factors and the greatest common factor (GCF). It provides examples of finding the factors of different numbers and identifying the common factors and GCF of sets of numbers. It includes practice problems for students to list the factors of numbers, find the common factors and GCF, and answer questions about factors and the GCF.

1. FACTORS
AND
Greatest Common Factor

2. What are the factors of 12?
, , , , ,1 2 12643
What are the factors of 81?
, , , ,1 3 819 27

3. Practice 1:
Identify the numbers that
are not factors of the numerals
given in a set.
1. 12 {1,2,3,4,5,6,10,12}
2. 24 {1,2,3,4,6,8,9,12,15,19,24}

4. 3. 35 {1,5,7,9,15,27,30,35}
4. 42 {1,2,3,6,7,14,21,25,42}
5. 50 {1,2,3,4,5,10,25,30,50}
6. 18 {1,2,3,4,5,6,9,18}
7. 64 {1,2,3,4,5,6,8,18,32,64}
8. 15 {1,2,3,4,5,15}

5. Practice 2:
Write the factors of the
given numbers.
1. 20 2. 36
3. 48 4. 50
5. 80

6. Answer key:
1. 20 = 1,2,4,5,10, 20
2. 36 = 1,2,3,4,6,9,12,18,36
3. 48 = 1,2,3,4,6,8,12,16,24,48
4. 50 = 1,2,5,10,25,50
5. 80 = 1,2,4,5,8,10,16,20,40,80

7. Practice 3:
Write T if the statement is
correct and F if the statement
is wrong.
1. 4 is the factor of 21
2. 1,3, and 4 are the only
factors of 12.

8. 3. 9 is not a factor of 99
4. 1,2,4, and 8 are the factors
of 8
5. 3 is a factor of 26
6. 1 is a factor of all numbers

9. What are the factors of 12?
, , , , ,1 2 12643
1 2 404 20
What are the factors of 40?
8 105

10. Therefore, the common
factors of 12 and 40 are…
1, 2, and 4
But the
Greatest Common Factor
is …. 4

11. What are the factors of 6?
, , ,1 632
1 3
What are the factors of 15?
, , ,
155
What are the factors of 9?
1 93

12. Therefore, the common
factors of 6, 9 and 15 are…
1 and 3
But the
Greatest Common Factor
is …. 3

13. Practice 1:
List all the factors of each
number in ascending order.
Then find the common factors
and Greatest Common Factor.

14. 1. 6 =
8 =
CF =
GCF =

15. Answer:
1. 6 = 1, 2, 3, 6
8 = 1, 2, 4, 8
CF = 1, 2
GCF = 2

16. 2. 9 =
18 =
CF =
GCF =

17. Answer:
2. 9 = 1, 3, 9
18 = 1, 2, 3, 6, 9,18
CF = 1, 3, 9
GCF = 9

18. 3. 12 =
15 =
CF =
GCF =

19. Answer:
3. 12 = 1, 2, 3, 4, 6, 12
15 = 1, 3, 5, 15
CF = 1, 3
GCF = 3

20. 4. 8 =
12 =
CF =
GCF =

21. Answer:
4. 8 = 1, 2, 4, 8
12 = 1, 2, 3, 4, 6, 12
CF = 1, 2, 4
GCF = 4

22. 5. 9 =
18 =
27 =
CF =
GCF =

23. Answer:
5. 9 = 1, 3, 9
18 = 1, 2, 3, 6, 9, 18
27 = 1, 3, 9, 27
CF = 1, 3, 9
GCF = 9

24. Practice 2:
Find the CF and GCF
1. 12 = 2. 27 =
18 = 36 =
CF= CF =
GCF = GCF =

25. 3. 15 = 4. 42 =
21 = 28 =
CF = CF =
GCF = GCF =

26. 5. 25 =
30 =
40 =
CF =
GCF =

27. Answers:
Find the CF and GCF
1. 12 = 1, 2, 3, 4, 6, 12
18 = 1, 2, 3, 6, 9, 18
CF = 1, 2, 3, 6
GCF = 6

28. 2. 27 = 1, 3, 9, 27
36 = 1, 2, 3, 4, 6, 9, 12, 18, 36
CF= 1, 3, 9
GCF = 9

29. 3. 15 = 1, 3, 5, 15
21 = 1, 3, 7, 21
CF = 1, 3
GCF = 3

30. 4. 42 = 1, 2, 3, 6, 7, 14, 21, 42
28 = 1, 2, 4, 7, 14, 28
CF = 1, 2, 7, 14
GCF = 14

31. 5. 25 = 1, 5, 25
30 = 1, 2, 3, 5, 6, 10, 30
40 = 1, 2, 4, 5, 8, 10, 20, 40
CF = 1, 5
GCF = 5

32. Assignment: Answer the ff.
___1. What is the sum of all
the factors of 18?
___2. What is the sum of all
the common factors of 24 and
16?

33. ___3. What is the GCF of two
consecutive numbers?
___4. What is the GCF of two
consecutive even numbers?
___5. What is the biggest
number that can exactly divide
12, 24, and 18?

34. __6. The GCF of two numbers
is 6. The second number is
three times the first number.
What are the two numbers?

35. T