GCF and Prime Factorization

Exponents, Prime Factorization, GCF, and LCM Review

Exponent

Base

Exponents

Drag and Drop

7^{6 -} In this expression, the 7 is the ​ ​

Placeholder

Drag these tiles and drop them in the correct blank above

base

exponent

addend

product

Drag and Drop

7^{6 -} In this expression, the 6 is the ​ ​

Placeholder

​

Drag these tiles and drop them in the correct blank above

exponent

addend

product

base

How to evaluate exponents

When evaluating an exponent, rewrite it as a multiplication problem, and then solve.

Example: 5³ = 5 x 5 x 5 = 125

Multiple Choice

$$7^3=$$

• 7 x 3 = 21

• 7 + 7 + 7 = 21

• 7 x 7 x 7 = 343

• 7 + 3 = 10

Multiple Choice

Evaluate: 4³ =

• 4 x 3 = 12

• 4 x 4 x 4 = 64

• 4 + 4 + 4 = 12

• 43

Multiple Choice

Evaluate 9⁴

• 9 x 4 = 36

• 90 x 90 = 8100

• 9 x 9 x 9 =729

• 9 x 9 x 9 x 9 = 6561

Multiple Choice

True or false:

The difference between an expression and an equation

is that an expression doesn't have an equal sign.

• True

• False

Prime Factorization

Prime factorization is decomposing (breaking down) a number to a product of just prime numbers.

Example: 36 = 2 x 2 x 3 x 3 = 2² x 3²

Labeling

What are the two missing factors?

Drag labels to their correct position on the image

2

5

3

6

Multiple Choice

What is the prime factorization of 50?

• 2 x 5 x 5
• 10 x 5
• 2 x 25
• 2 x 10 x 5

Multiple Choice

What is the prime factorization of 24?

• 2 x 2 x 2 x 4
• 2 x 2 x 3 x 3
• 2 x 2 x 2 x 3
• 2 x 2 x 6

Multiple Choice

What is the prime factorization of 60?

• 2 x 2 x 2 x 5
• 2 x 3 x 3 x 5
• 2 x 2 x 2 x 3
• 2 x 2 x 3 x 5

Greatest Common Factor

GCF

The biggest integer that evenly divides into two or more numbers.
(Remember, Factor = Fewer)
Example:
Factors of 8: 1, 2, 4, 8
Factors of 12: 1, 2, 3, 4, 6, 12

The GCF of 8 and 12 is 4.

Fill in the Blanks

Based on this information, what is the GCF of 12 and 20?

12: 1, 2, 3, 4, 6, 12

20: 1, 2, 4, 5, 10, 20

Dropdown

What is the GCF of 24 and 36?



24: 1, 2, 3, 4, 6, 8, 12, 24

36: 1, 2, 3, 4, 6, 9, 12, 18, 36



GCF = ​ ​

Select answer

Fill in the Blanks

What is the GCF and 25 and 10?

LCM is the smallest number that both can multiply evenly into.

(Reminder, multiple = more)

​

​Least Common Multiple

Match

Match the following

• Multiples of 3

• Multiples of 5

• Multiples of 6

• Multiples of 2

• Multiples of 9

3, 6, 9, 12, 15...

5, 10, 15, 20, 25...

6, 12, 18, 24, 30...

2, 4, 6, 8, 10, 12...

9, 18, 27, 36, 45...

• 3, 6, 9, 12, 15...

• 5, 10, 15, 20, 25...

• 6, 12, 18, 24, 30...

• 2, 4, 6, 8, 10, 12...

• 9, 18, 27, 36, 45...

Multiple Choice

What is the Least Common Multiple (LCM) of 3 and 8?

3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48

8: 8, 16, 24, 32, 40, 48

• 3

• 8

• 24

• 48

Fill in the Blanks

What is the LCM of 9 and 12?

Match

Match the following

• Multiples mean

• Factors mean

• LCM stands for...

• GCF stands for...

more!

(Example: 3: 3, 6, 9, 12, 15, 18)

fewer!

(Example: 12: 1, 2, 3, 4, 6, 12)

Least Common Multiple

Greatest Common Factor

• more!

  (Example: 3: 3, 6, 9, 12, 15, 18)

• fewer!

  (Example: 12: 1, 2, 3, 4, 6, 12)

• Least Common Multiple

• Greatest Common Factor