Prime Factorization and Exponents

LCm and GCF using exponents

by AnneMarie Grayburn

​GCF using exponents

• Write the prime factors using exponents

• Look at which factors they share

  • 2, 3, and 5 in the example ​-->

• ​From the shared factors, choose the smaller exponent

  • ​Circled in red

• ​Multiply those together

​LCM Using Exponents

• ​This time, choose the highest exponent of shared factors

• ​Also include the factors they don't share

• Example​

  • 12 and 90 share 2 and 3

  • ​They don't share 5

  • ​Choose

  • ​Multiply:

Multiple Select

Which factors do they share? Select all.

$$120=2^3\times3\times5$$  

$$2100=2^2\times3\times5^2\times7$$  

• 2

• 3

• 5

• 7

Open Ended

What should you multiply to find the GCF?

$$120=2^3\times3\times5$$  

$$2100=2^2\times3\times5^2\times7$$  

​GCF of 120 and 2100

Choose 2², 3, 5

​

​Multiply together: 2² * 3 * 5 = 30

Multiple Choice

Use the prime factorization to find the GCF of 588 and 280.

$$588=2^2\times3\times7^2$$  

$$280=2^3\times5\times7$$  

• 5880

• 420

• 14

• 28

Open Ended

What should you multiply to find the LCM?

$$120=2^3\times3\times5$$  

$$2100=2^2\times3\times5^2\times7$$  

​GCF of 120 and 2100

Choose 2³, 3, 5², 7

​

​Multiply together:

Multiple Choice

Use the prime factorization to find the LCM of 588 and 280.

$$588=2^2\times3\times7^2$$  

$$280=2^3\times5\times7$$  

• 5880

• 420

• 14

• 28