Greatest Common Factor

Greatest Common Factor (GCF)

Vocabulary

1. Factors- #'s multiplied together to get a product. (5x2=10, 5 and 2 are factors of 10)

2. Greatest common factor- the largest factor that two or more numbers have in common.

3. prime numbers- #'s with exactly 2 factors. (2,3,5,7,11,13,17,...)

4. composite numbers- #'s with more than 2 factors. (4,6,8,9,10,12,14,...)

Poll

Is the number 0 prime, composite, or neither?

• prime

• composite

• neither

Poll

Is the number 1 prime or composite?

• prime

• composite

• neither

Special cases 0 and 1:

If all numbers are either prime or composite, what about 0 and 1?

0 is considered neither prime or composite because 0 has an infinite number of factors. Every number is a factor of 0.

1 is considered neither prime or composite because 1 has only one factor (1). When you have a double factor then you only use it as a factor one time.

Is each number prime, composite, or neither?

• 45

• 19

• 100

• 22

• 0

• 51

Divisibility Rules: Shortcuts to help determine if numbers are factors of a number.

• 2 - is the last digit an even number

• 3 - is the sum of the digits divisible by 3

• 4 - are the last 2 digits divisible by 4

• 5 - is the last digit a 0 or 5

• 6 - is the number divisible by both 2 and 3

• 9 - is the sum of the digits divisible by 9

• 10 - is the last digit a 0

Steps to find the GCF:

• Find ALL factors of each number.

• Write the factors in numerical order from least to greatest.

• Find the common factors (CF)

• The greatest of the common factors is the GCF.

• Show all work in a neat and orderly way.

Find the GCF of 12 and 20

Factors of 12                     Factors of 20
1 x 12                                      1 x 20            

2 x 6                                        2 x 10                        

3 x 4                                        4 x 5 

12 = 1, 2, 3, 4, 6, 12
20 = 1, 2, 4, 5, 10, 20

Common factors (CF) of 12 and 20
CF = 1, 2, 4
GCF = 4

Practice:

What is the GCF of 24 and 40?

24 =

40 =

CF =

GCF =

What is the GCF of 9 and 22?

9 =

22 =

CF =

GCF =

Multiple Select

EXIT TICKET

If all numbers are either prime or composite, what about 0?

• prime, because 0 has exactly 2 factors

• composite, because 0 has more than two factors

• neither, because 0 has infinite number of factors.

Poll

Do you understand today's lesson?

• Yes, I totally got this!

• I have no idea how to do this.

• I need to practice a little to understand better.