1. Greatest
Common
Divisor

2. Greatest Common Divisor
List all the positive divisors of the following. 20 40 1 20 1 40
Make a list! 2 10 2 20 4 5 4 10 5 8

3. Greatest Common Divisor
To find divisors of a number make a list starting with the lowest possible factor which is 1.
We start with 1 and work our way up. We know we didn’t miss any factors because our list is organized.

4. Greatest Common Divisor
When two numbers have the same divisor it is called a common divisor.
Can you think of a common divisor for 12 and 6?
1, 2, 3 or 6

5. Greatest Common Divisor
GCD-
Largest
number that divides evenly into a given set of numbers.
Greatest Common Divisor-
It is useful to know this for reducing fractions.
There are two ways to find the GCD

6. Greatest Common Divisor
Method # 1 List all the divisors of both numbers. Then find the greatest common divisor.
Divisors of 12
1 x 12
2 x 6
3 x 4
Divisors of 30
1 x 30
2 x 15
3 x 10
5 x 6
Ex.
Common Divisors are 1,2,3,6
GCD= 6

7. Make a List Greatest Common Divisor60 84
This method is only useful if both numbers are small 1 60 1 84 2 30 2 42 3 20 3 28 4 15 4 21 5 12 6 14 6 10 7 12
GCD = 12

8. Greatest Common Divisor
Method #1 is great, but you have to list all of the divisors for both numbers!
This can sometimes take a while!
That’s why there is
Method # 2

9. Greatest Common Divisor
Find the prime factorization of the two numbers. Then multiply their common factors. 12 30 2 6 2 15 2 3 3 5
2 and 3
Divisors the 2 numbers have in common are:
Multiply the common factors.
GCD = 2 x 3 = 6

10. Greatest Common Divisior
Prime Factorization 60 84 2 30 2 42 2 15 2 21 3 5 3 7
GCD = 2 x 2 x 3=12

11. Greatest Common Divisor
Prime Factorization 20 24 2 10 2 12 2 5 2 6 2 3
GCD = 2 x 2 = 4

12. GCD= 6 Common Divisors are 1,2,3,6 GCD, Make a List Method #1
GCD is the largest number that is a divisors of 2 numbers. It is useful to know this for reducing fractions.
Step 1: List all the divisors of both numbers.
Step 2: Then find the greatest common divisor.
Divisors of 12
1 x 12
2 x 6
3 x 4
Divisors of 30
1 x 30
2 x 15
3 x 10
5 x 6
Ex.
GCD= 6
Common Divisors are 1,2,3,6
This method is only useful if both numbers are small

13. Step 1: Find the prime factorization of the 2 numbers.
Step 2: Then multiply their common factors. 12 30 2 6 2 15 2 3 3 5
Factors the 2 numbers have in common are:
2 & 3
Multiply the common factors.
GCD = 2 x 3 = 6

14. Try these Find GCD of 30 and 75 Find GCD of 42 and 105