Factors and Multiples - Mrs Pittman

Factors and Multiples

Factors

• Factors are numbers that divide evenly into another number.  For example 8 is a factor of 24 because 8 divides evenly into 24.  8 is not a factor of 30 because 8 does not divide evenly into 30.

Poll

5 is a factor of 30

• True!

• False!

Multiple Select

12 is a factor of which numbers? Pick all that are correct.

• 24

• 36

• 4

• 6

Multiple Choice

The definition of factor:

• a smaller number

• a number that divides into another with a remainder

• a number that divides into another evenly

Factors are used to help make even groups by dividing things up evenly.

• If there are 10 girls and 15 boys and I want to put them in groups, I can put them in groups of 1's or groups of 5's.  No other options will work if I want the groups to be even.  

• If I have 16 carnations and 32 roses and I want to make identical bouquets with them, I can make 1 large bouquet, 2 bouquets, 4 bouquets, 8 bouquets, or 16 bouquets because 1, 2, 4, 8, and 16 are common factors of 16 and 32. 

Greatest Common Factor

• The GCF of two or more numbers is the largest factor they have in common.

• If I look at all of the common factors of 16 and 32, I see that 16 is the greatest of their common factors.

• 16:  1, 2, 4, 8, 16

• 32:  1, 2, 4, 8, 16, 32

Multiple Choice

The GCF of 18 and 24 is:

18: 1, 2, 3, 6, 9, 18

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

• 24

• 6

• 18

• 1

Multiple Choice

What is the GCF of 14 and 21?

• 1

• 3

• 7

• 21

Multiple Choice

What is the GCF of 24 and 32?

• 1

• 4

• 8

• 16

GCF and Distributive Property

• We can also use GCF to rewrite addition.

• 18 + 30 becomes 6(3 + 5).

• 6 is the gcf of 18 and 30. Divide both by 6 and write what you have left in parentheses.

Multiple Choice

Rewrite the sum using the GCF and distributive property:

20 + 24

• 2(10 + 12)

• 4(5 + 6)

Multiples:  to find a multiple, multiply a number by 1, then 2, then 3, then 4, etc.

• The multiples of 7:  7, 14, 21, 28, 35....they go to infinity!

• The multiples of 9:  9, 18, 27, 36... etc.... 

Poll

14 is a multiple of 7

• True

• False

All numbers share common multiples. 

• 8:  8, 16, 24, 32, 40, 48, 56, 64, etc...

• 3:  3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, etc...

• They share many multiples.  The first two I see are 24 and 48.  Because multiples go to infinity, so do common multiples.  

• The FIRST multiple they have in common is special. It is called the LCM.

LCM:  Least common multiple

• 5:  5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, etc...

• 10:  10, 20, 30, 40, 50, 60, 70, 80, 90, etc...

• The first multiple they have in common is 10!  10 is called the least of their common multiples or LCM.  

Multiple Choice

The LCM of 12 and 14:

12: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, etc...

14: 14, 28, 42, 56, 70, 84, 98, 112, etc...

• 12

• 14

• 84

• 120

Multiple Choice

The LCM of 8 and 14 is:

8: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, etc...

14: 14, 28, 42, 56, 70, 84, 98, etc...

• 8

• 14

• 56

• 96

Least Common Multiple is very useful when I am trying to match up numbers.

• If I have to buy the same number of pens and pencils when pencils come in packages of 8 and pens come in packages of 10, then I would buy a total of 40 of each.  Or I could by 80 of each.  Or 120 of each.  40 is the least number I could buy and 40 is their LCM.

Multiple Choice

Hamburgers come in packages of 4 and buns come in packages of 12. What is the least number of burgers and buns I need to buy so that I have the exact same amount of burgers and buns?

• 12

• 24

• 1

• 2

Multiple Choice

I need the same amount of hats and tshirts. What is the least number of each I can buy if hats come in boxes of 7 and tshirts come in boxes of 9?

• 1 of each

• 63 of each

• 42 of each

• 18 of each

Greatest common factors are small while Least common multiples are large.  This can be confusing.  

• Factors of 24:  1, 2, 3, 4, 6, 8, 12, 24

• Multiples of 24:  24, 48, 72, 96, 120,  and on to infinty.....

Multiple Choice

Find the GCF of 8 and 12

• 4

• 24

Multiple Choice

Find the LCM of 8 and 12

• 4

• 24

Multiple Choice

Find the LCM of 16 and 12

• 4

• 48

Multiple Choice

Find the GCF of 16 and 12

• 4

• 48