Prime Factorization, GCF and LCM

Prime Factorization, GCF,

LCM

Prime Factorization

Things to remember:

●Whole numbers greater than 1 are either prime or composite numbers.

●A composite number can be written as a product of its prime factors, called its
prime factorization.

Let’s try it…

48

Popsicle stick time!

56

33

32

Multiple Choice

What is the prime factorization of 24?

• 2x2x2x2x3

• 2x2x3

• 3x3

• 2x2x2x3

Multiple Choice

What is the prime factorization of 8?

• 2x4

• 2x2x2

• 2x2x2x2

• 8x1

Greatest Common Factor

●The Greatest Common Factor, or GCF, is the greatest number that is a factor
of 2 or more numbers.

●You will use what you have learned about prime factorization to find the GCF.

Let’s try together first!

What is the GCF of 18 and 24?

Get ready! Popsicle sticks!

18, 36

22, 55

100, 48

Fill in the Blank

What is the greatest common factor of 12 and 30?

Fill in the Blank

What is the greatest common factor of 18 and 4?

Fill in the Blank

What is the greatest common factor of 12 and 16?

Fill in the Blank

What is the greatest common factor of 15 and 6?

Fill in the Blank

What is the greatest common factor of 27 and 30?

Fill in the Blank

What is the greatest common factor of 36 and 32?

Fill in the Blank

What is the greatest common factor of 10 and 15?

Least Common Multiple

●The Least Common Multiple, or LCM, is the least multiple, not including zero,
common to both numbers.

●ONE WAY to do this:

○Start listing the multiples of each number until you find one that they have in common.

●ANOTHER WAY to do this:

Let’s try the first way to solve:

List the multiples of each number until you find one that they have in common.

8, 12

Popsicle Sticks!

2, 5

8, 10

5, 8

Now let’s talk about the other way we could solve:

Find the LCM of 12 and 10.

Since this is pretty new, let’s do one more together:

Find the LCM of 3 and 7.

Popsicle Sticks!

8, 12

6, 7

3, 4

Fill in the Blank

What is the least common multiple of 3 and 16?

Fill in the Blank

What is the least common multiple of 6 and 9?

Fill in the Blank

What is the least common multiple of 9 and 2?

Fill in the Blank

What is the least common multiple of 9 and 4?

Fill in the Blank

What is the least common multiple of 4 and 16?

Fill in the Blank

What is the least common multiple of 6 and 16?

Exit Ticket time!

On the paper that I am about to give you, answer the 4 questions. This must be turned in before you leave!

1. Write the prime factorization of 84.

2. Select all the prime numbers.

3

9

13

23

33

3. What is the greatest common factor of 12 and 54?

4. What is the LCM of 3 and 7?

Q 3-2