Introduction to Common Factors and Multiples

Factors and Multiples

Let's try something new!

GREATEST

COMMON

FACTOR

• To find the GREATEST COMMON FACTOR, we use the prime factorization and look for over lapping prime factors

• OR you can list all the factors and find the LARGEST factor that overlaps (this is risky, because it is easy to forget a factor)

• Numbers with no factors in common have a GCF of 1

Multiple Select

Select all factors of 6

• 1

• 2

• 3

• 4

• 6

Multiple Select

What is the prime factorization of 18?

• 2 x 2 x 2 x 3

• 2 x 3 x 3

• 3 x 3 x 3

• 6 x 3

Multiple Choice

What is the greatest common factor of 12 and 18?

• 2

• 4

• 12

• 6

Fill in the Blanks

What is the greatest common factor of 30 and 45?

LEAST

COMMON

MULTIPLE

• To find the least common multiple, list several multiples of each number and circle the SMALLEST number they have in common!

• Numbers that are "relatively prime" have no factors in common and their product will be the least common multiple.

Multiple Select

Check all boxes that show a multiple of 8.

• 8

• 12

• 16

• 24

• 30

Multiple Choice

What is the least common multiple of 8 and 6?

• 14

• 12

• 48

• 24

Multiple Choice

What is the least common multiple of 7 and 9.

• 16

• 54

• 63

• 81

GCF/LCM word problems

• If it asks for the "maximum" or the "largest number of groups", you will use the GCF

• If you are looking for overlapping dates or amounts that are bigger than the numbers given, you will use the LCM

• Think about what is "reasonable"

Multiple Choice

Fresh produce is delivered to a restaurant every 4 days. Every 6 days, the restaurant receives a delivery of dried and canned goods. If the produce and dried and canned goods were delivered today, how many days will pass until they are all delivered to the restaurant on the same day again? (hint, we are looking for overlap, use LCM)

• 2 days

• 6 days

• 12 days

• 24 days

Multiple Choice

Miki has 104 nickels and 88 dimes. She wants to divide her coins into groups where each group has the same number of nickels and the same number of dimes. What is the largest number of groups she can have?

• 13

• 11

• 8

• 4

Multiple Choice

1 is a prime number.

• True

• False.

Multiple Choice

Choose the smallest prime number.

• 5

• 3

• 2

Multiple Choice

Which of the following is correct prime factorization of 12?

• $$2\times6$$  

• $$1\times12$$  

• $$2\times2\times3$$  

• $$3\times4$$  

Multiple Choice

Find the prime factorization of 18

• 2 • 9

• 2² • 3

• 2 • 3²

• 3 • 6

Multiple Choice

Find the prime factorization of 30

• 2² • 5 • 7

• 2 • 3²

• 2 • 3 • 7

• 2 • 3 • 5