The document discusses prime factorization, factor trees, greatest common factors (GCF), and least common multiples (LCM). It provides examples of breaking numbers down into their prime factors using factor trees. It then explains how to find the GCF of two numbers by identifying their common prime factors. Similarly, it describes how to find the LCM of two numbers by multiplying their common prime factors together with all other unique factors.

1. PRIME FACTORIZATION GCF & LCM

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

4. Prime Factorization Factor 225

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 THE COMMON FACTORS ARE 5 & 3 225 5 45 5 9 5 • 5 • 3 • 3 3 10 30 3 • 5 • 2

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

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

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

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

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 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 5•5•7 2•5•3 None Only 2 is in common

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

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

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