1. PRIME FACTORIZATION GCF & LCM

2. FACTORING Factoring is the opposite of multiplying
A Factor Times another Factor Equals a Product
A Composite Number can be factored by two or more numbers
Factoring is breaking Down a Product into it’s Factors
Prime Factorization is breaking down a Product into it’s Prime Factors.

3. FACTOR TREE
A factor tree breaks a product down into it’s Prime Factors. It is called PRIME FACTORIZATION
PRODUCT 30 3 10
3 •
2 • 5
PRIME FACTORS

4. Prime Factorization
Factor 225

5. Prime Factorization
Factor 225
Put number on top of factor tree.
225

6. Prime Factorization Factor 225 Put number on top of factor tree. 225
Find factors and branch down tree
225
5 • 5 • 3 • 3 = 32 • 52

7. GCF - Greatest Common Factor
The GCF of two numbers is the greatest number that divides into both numbers evenly.
Ex: The GCF of 14 & 35 is 7, since 7 is the greatest number that goes into both 14 & 35 evenly

8. HOW TO FIND THE GCF
The key to determining the GCF is to identify Common Factors in Both Numbers and Multiplying them together.

9. COMMON FACTORS OF 225 & 30
225 30
3 • 5 • 2
5 • 5 • 3 • 3
THE COMMON FACTORS ARE 5 & 3

10. IDENTIFY COMMON FACTORS
3 • 5 • 2
7 • 5 • 2 • 17

11. IDENTIFY COMMON FACTORS
3 • 5 • 2
7 • 5 • 2 • 17
THE COMMON FACTORS ARE 5 & 2

12. IDENTIFY COMMON FACTORS
7 • 5 • 5 • 3 • 3
2 • 5 • 2 • 5 • 7

13. IDENTIFY COMMON FACTORS
7 • 5 • 5 • 3 • 3
2 • 5 • 2 • 5 • 7
THE COMMON FACTORS ARE 7 & 5 & 5

14. IDENTIFY COMMON FACTORS
7 • 5 • 5 • 3 • 3
&
2 • 5 • 2 • 5 • 7
2 • 11 • 5 • 3 • 7
&
13 • 3 • 2 • 5 • 2
3 • 5 • 11 • 3 • 3
&
2 • 2 • 2 • 17 • 7
5 • 5 • 7 • 3
&
2 • 5 • 2 • 3
&
2 • 5 • 2 • 7
For three numbers common factors must be in all three numbers

15. IDENTIFY COMMON FACTORS
5•5•7
7 • 5 • 5 • 3 • 3
&
2 • 5 • 2 • 5 • 7
2 • 11 • 5 • 3 • 7
&
13 • 3 • 2 • 5 • 2
2•5•3
None
3 • 5 • 11 • 3 • 3
&
2 • 2 • 2 • 17 • 7
5 • 5 • 7 • 3
&
2 • 5 • 2 • 3
&
2 • 5 • 2 • 7
For three numbers common factors must be in all three numbers
Only 2 is in common

16. Finding Greatest Common Factor
Find GCF of 225 & 30

17. Finding Greatest Common Factor
Find GCF of 225 & 30
225
Complete Factor Tree for both numbers. 30
3 • 5 • 2
5 • 5 • 3 • 3

18. Finding Greatest Common Factor
Find GCF of 225 & 30
225
Complete Factor Tree for both numbers.
Identify Common Factors. 30
3 • 5 • 2
5 • 5 • 3 • 3
THE COMMON FACTORS ARE 5 & 3

19. Finding Greatest Common Factor
Find GCF of 225 & 30
225
Complete Factor Tree for both numbers.
Identify Common Factors.
Multiply Common Factors for GCF 30
3 • 5 • 2
5 • 5 • 3 • 3
THE COMMON FACTORS ARE 5 & 3
GCF = 5 • 3 = 15

20. Finding the LCM Least Common Multiple
The LCM is the Lowest Number that is a Multiple of Both Numbers.
Ex. The LCM of 12 & 9 is 36 since both 12 & 9 divide evenly into 36.
Hint: Think of Common Denominators in Fractions.
A common denominator is the
LCM of the denominators.

21. Finding the LCM Least Common Multiple

22. Finding Least Common Multiple
Find LCM of 45 & 25

23. Finding Least Common Multiple
Find LCM of 45 & 25 45 75
Complete Factor Tree for both numbers.
5 • 3 • 3
5 • 5 • 3

24. Finding Least Common Multiple
Find LCM of 45 & 25 45 75
Complete Factor Tree for both numbers.
Identify Common Factors.
5 • 3 • 3
5 • 5 • 3
THE COMMON FACTORS ARE 5 & 3

25. Finding Least Common Multiple
Find LCM of 45 & 25 45 75
Complete Factor Tree for both numbers.
Identify Common Factors.
Multiply Common Factors with ALL OTHER FACTORS
5 • 3 • 3
5 • 5 • 3
THE COMMON FACTORS ARE 5 & 3
OTHER FACTORS
LCM = CF’s•ALL OTHER FACTORS
LCM = 5•3 • 5 • 3 = 225

26. Finding Least Common Multiple
Find LCM of 12 & 34
Complete Factor Tree for both numbers.
Identify Common Factors.
Multiply CF’s with ALL OTHER FACTORS

27. Finding the LCM Least Common Multiple (FOR 3 NUMBERS)
Find LCM of 225, 10 & 66

28. Finding the LCM Least Common Multiple (FOR 3 NUMBERS)
Find LCM of 225, 10 & 66
225
Complete Factor Tree for all numbers. 10 66
5 • 2
11 • 3 • 2
5 • 5 • 3 • 3

29. Finding the LCM Least Common Multiple (FOR 3 NUMBERS)
Find LCM of 225, 10 & 66
225
Complete Factor Tree for all numbers.
Identify Common Factors OF ANY 2 #’S. 10 66
5 • 2
11 • 3 • 2
5 • 5 • 3 • 3
THE COMMON FACTORS ARE 2,5 & 3

30. Finding the LCM Least Common Multiple (FOR 3 NUMBERS)
Find LCM of 225, 10 & 66
225
Complete Factor Tree for all numbers.
Identify Common Factors OF ANY 2 #’S.
Multiply Common Factors with ALL OTHER FACTORS 10 66
5 • 2
11 • 3 • 2
5 • 5 • 3 • 3
THE COMMON FACTORS ARE 2,5 & 3
OTHER FACTORS
LCM=2•5•3•5•3•11=4950