1. Greatest common factor
Mr. Hendy Industries

2. WALT: Find the Greatest Common Factor between different numbers
Learning goal
WALT: Find the Greatest Common Factor between different numbers

3. Two methods for finding the gcf
Factor Search
Prime Factorization
List factors
24: 1, 2, 3, 4, 6, 8, 12, 24
36: 1, 2, 3, 4, 5, 6, 9, 12, 18, 36
GCF = 12
Factor trees for both numbers, then multiply prime numbers
Prime factors for 24 and 36
24: 2 x 2 x 2 x 3
36: 2 x 2 x 3 x 3
GCF = 2 x 2 x 3 = 12

4. Factor search

5. Step #1: list the factors
What numbers can we multiply together to equal our base number? What factors does our base number have?
12: 1, 2, 3, 4, 6, 12

6. Step #2: Circle the largest factor that both numbers have in common
12: 1, 2, 3, 4, 6, 12 24: 1, 2, 3, 4, 6, 8, 12, 24

7. GCF = 12 Step #3: record the gcf 12: 1, 2, 3, 4, 6, 12
After you have listed all the factors for your numbers and circled the Greatest Common Factor (GCF), record the GCF
12: 1, 2, 3, 4, 6, 12
24: 1, 2, 3, 4, 6, 8, 12, 24
GCF = 12

8. Some examples
Find the GCF of 20 and 30

9. Some examples
Find the GCF of 17 and 25

10. Some examples
Find the GCF of 15, 45, and 30

11. Challenge!

12. Challenge!
15 and 33
15 and 33

13. Challenge! Gcf = 3
15 and 33
15 and 33

14. Challenge!

15. Challenge!
40 and 18
40 and 18

16. Challenge! Gcf = 2
40 and 18
40 and 18

17. Consolidation 10 and 25 42 and 16 36 and 21 5 and 40 18 and 54
Find the GCF for the following sets of numbers
10 and 25
42 and 16
36 and 21
5 and 40
18 and 54
24, 12 and 36

18. Consolidation
10 and 25 GCF = 5
42 and 16 GCF = 2

19. Consolidation
36 and 21 GCF = 3
5 and 40 GCF = 5

20. Consolidation
18 and 54 GCF = 18
24, 12, and 36 GCF = 12

21. Success criteria
I am successful when I can…

22. Finding GCF using Prime Factorization
But wait! There’s more…
Finding GCF using Prime Factorization

23. Step #1: create a factor tree for your numbers12 24 2 6 3 2 12 2 6 3 2 2

24. Step #2: List out all prime factors
12: 2 x 2 x 3 24: 2 x 2 x 2 x 3

25. Step #3: circle each pair of identical prime factors
12: 2 x 2 x 3 24: 2 x 2 x 2 x 3

26. Step #4: multiply the prime factors together to get your gcf
2 x 2 x 3 = 12 Therefore the GCF between 12 and 24 is 12

27. Lowest Common Multiple
Mr. Hendy Industries

28. WALT: Find the Lowest Common Multiple between numbers
Learning goal
WALT: Find the Lowest Common Multiple between numbers

29. What is a multiple? 5 x 1 = 5 5 x 2 = 10 5 x 3 = 15 5 x 4 = 20
Let’s say we start with the number 5. Every time we multiply 5 by another number, we create a MULTIPLE. Watch…
5 x 1 = 5
5 x 2 = 10
5 x 3 = 15
5 x 4 = 20
5 x 5 = 25
Therefore: 5, 10, 15, 20, 25
are multiples of 5

30. Lowest common multiple
To find the Lowest Common Multiple between numbers, we need to list multiples for both numbers until we find one that is the same between them. For example…
4: 4, 8, 12, 16, 20
5: 5, 10, 15, 20

31. Some examples
Find the LCM of 15 and 4

32. Some examples
Find the LCM of 15 and 4 LCM = 60

33. Some examples
Find the LCM of 13 and 16

34. Some examples
Find the LCM of 13 and LCM = 208

35. Find the LCM of the following numbers
practice
Find the LCM of the following numbers
8 and 6
12 and 6
7 and 15
9 and 6
13 and 18
20 and 45

36. Consolidation
8 and 16 LCM = 16
12 and 6 LCM = 12

37. Consolidation
7 and 15 LCM = 105
9 and 6 LCM = 18

38. Consolidation
13 and 18 LCM = 234
20 and 45 LCM = 180

39. Success criteria
I am successful when I can…