1. Used to find the LCM and GCF to help us add and subtract fractions.
Prime Factorization
Used to find the LCM and GCF to help us add and subtract fractions.

2. Factors
A factor is a number that divides another number with no remainder.
Examples: factors of 12 are 1 & 12, 2 & 6, 3 & 4

3. Prime numbers A number that has only two factors, 1 and itself.
Examples: 2, 3, 5, 7, 11, 13, 17…

4. Prime Factorization
The prime factorization of a number is the product of its prime factors.
Example: of 12- or

5. Factor Trees
Use a factor tree to break down a number to get to the prime numbers (till you can’t break it down anymore) or

6. Another example

7. One more example…

8. Now you try …
Find the prime factorization of: 40 48

9. GCF
The Greatest Common Factor between at least two numbers… used to simplify fractions.

10. GCF
The greatest common factor of two or more numbers is the greatest factor that is in common to those numbers.
The GCF can be found by:
Listing all the factors of each number and then finding the largest number in all lists to give the GCF.
Do a factor tree of each number and the prime factors that are in all trees multiply to give the GCF.

11. Listing all the factors…
This works best when the numbers are small and have few factors.
12 and 15
Factors of 12: 1, 2, 3, 4, 6, 12
Factors of 15: 1, 3, 5, 15
GCF= 3

12. Do a factor tree…
This works best when the numbers are large and have many factors.
These two trees
share a 3 and 5.
Multiply these
two together
and get 15.
GCF=15

13. Try another with a factor tree
45 and 81
GCF=3x3=9

14. Now you try… Find the GCF
16 and 24
12, 48, 72

15. LCM
Least Common Multiple between at least two numbers… used to find a common denominator to help add and subtract fractions.

16. Multiple
The multiple of a number is a product of that number and a whole number…
Meaning multiply!
Multiples of 5:
5, 10, 15, 20, 25, 30…
Multiples of 3:
3, 6, 9, 12, 15, 18, 21…

17. LCM
Least Common Multiple is the smallest multiple of two or more numbers.
The easiest way to find the LCM:
Start to list all the multiples of the numbers involved and stop as soon as you have a number in common to both lists.
Ex: between 3 and 5
5, 10, 15, 20…
3, 6, 9, 12, 15…
So the LCM is 15!

18. You try it! Find the LCM between 4 and 9
Make a list of multiples of each number.
4, 8, 12, 16, 20, 24, 28, 32, 36, 40
9, 18, 27, 36..
LCM = 36!