factors & multiples. essential question: how can we determine if a number is prime or composite?...

FactorsFactors&&

MultiplesMultiples

Essential Question:Essential Question:How can we determine if a number How can we determine if a number

is prime or composite?is prime or composite?

Common Core Objective:Common Core Objective:6.NS.26.NS.2

Common Core Objective:Common Core Objective:Students will be able to describe the Students will be able to describe the

difference between a prime and composite difference between a prime and composite number and use book ends to determine number and use book ends to determine the list of factors for a given number with the list of factors for a given number with 80% accuracy.80% accuracy.

Factors & MultiplesFactors & Multiples

Vocabulary: Factor – a number that divides into a

whole number with a remainder of zero. Prime Number – a whole number that

has exactly two unique factors, 1 and the number itself.

Composite Number – a number greater than 1 with more than two factors.

Prime Factorization – a composite number expressed as a product of prime numbers.


Before we get started lets do a Before we get started lets do a little brain activity…little brain activity…

Lets name all the different numbers we Lets name all the different numbers we can multiply to get 28can multiply to get 28

1 x 281 x 282 x 142 x 144 x 74 x 7

Well guess what, these numbers have a Well guess what, these numbers have a special name…they’re called factors.special name…they’re called factors.

Factors come in pairs…like for the number Factors come in pairs…like for the number 28.28.


A A PRIMEPRIME number is… number is…A number with only two factors, 1 and A number with only two factors, 1 and

itself.itself.

Some Examples: 2, 3, 5, 7, 11, 13Some Examples: 2, 3, 5, 7, 11, 13

A A COMPOSITECOMPOSITE number is… number is…

A number with more than 2 factors.A number with more than 2 factors.

Some Examples: 6, 8, 9, 10, 12, 14, 15Some Examples: 6, 8, 9, 10, 12, 14, 15


Finding Factors of a NumberFinding Factors of a NumberExample 1Example 1:: Find the factors of 12. Is Find the factors of 12. Is

it prime or composite?it prime or composite?





1 x 12




1 x 12

2 x 6




1 x 12

3 x 4

2 x 6




1 x 12

3 x 4

2 x 6

1212: 1, 2, 3, 4, : 1, 2, 3, 4, 6, 126, 12CompositeComposite




1 x 24




2 x 121 x 24




2 x 12

3 x 8

1 x 24




2 x 12

4 x 6

3 x 8

1 x 24




2 x 12

4 x 6

3 x 8

2424: 1, 2, 3, 4, 6, 8, 12, : 1, 2, 3, 4, 6, 8, 12, 2424

1 x 24

CompositeComposite




1 x 17

Finding Factors of a NumberFinding Factors of a NumberExample 3Example 3:: Find the factors of 17 and Find the factors of 17 and

then identify as prime or composite.then identify as prime or composite.


1 x 17

1717: 1, : 1, 1717PrimePrime



Two is a VERY special number for a reason Two is a VERY special number for a reason

we are about to see…we are about to see…







1 x 2 22: 1, 2: 1, 2





Two is the Two is the ONLY EVEN PRIME ONLY EVEN PRIME NUMBERNUMBER!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

wow that is awesome!wow that is awesome!


1 x 2 22: 1, 2: 1, 2

Finding multiples is just like Finding multiples is just like multiplying the number by 1, then multiplying the number by 1, then

2, then 3, then 4, and so on…2, then 3, then 4, and so on…

This is why it called finding the This is why it called finding the MULTIPLESMULTIPLES

(you are MULTIPLying)(you are MULTIPLying)


Finding Multiples of a NumberFinding Multiples of a NumberExample 5Example 5:: Find the first five Find the first five

multiples of 8.multiples of 8.




8 x 1 = 88 x 1 = 8

8 x 2 = 168 x 2 = 16

8 x 3 = 248 x 3 = 24

8 x 4 = 328 x 4 = 32

8 x 5 = 408 x 5 = 40




8 x 1 = 88 x 1 = 8

8 x 2 = 168 x 2 = 16

8 x 3 = 248 x 3 = 24

8 x 4 = 328 x 4 = 32

8 x 5 = 408 x 5 = 40


Therefore…to express Therefore…to express the first five multiples of the first five multiples of 8, your answer would 8, your answer would look like:look like:



8 x 1 = 88 x 1 = 8

8 x 2 = 168 x 2 = 16

8 x 3 = 248 x 3 = 24

8 x 4 = 328 x 4 = 32

8 x 5 = 408 x 5 = 40


88: 8, 16, 24, 32, : 8, 16, 24, 32, 40, …40, …

Therefore…to express Therefore…to express the first five multiples of the first five multiples of 8, your answer would 8, your answer would look like:look like:

Finding Multiples of a NumberFinding Multiples of a NumberExample 6Example 6:: Find the first 8 multiples Find the first 8 multiples

of 15.of 15.


Finding Multiples of a NumberFinding Multiples of a Number

Example 6Example 6:: Find the first 8 multiples of 15. Find the first 8 multiples of 15.

15 x 1 = 1515 x 1 = 15

15 x 2 = 3015 x 2 = 30

15 x 3 = 4515 x 3 = 45

15 x 4 = 6015 x 4 = 60

15 x 5 = 7515 x 5 = 75

15 x 6 = 9015 x 6 = 90

15 x 7 = 10515 x 7 = 105

15 x 8 = 12015 x 8 = 120



Example 6Example 6:: Find the first 8 multiples of 15. Find the first 8 multiples of 15.

15 x 1 = 1515 x 1 = 15

15 x 2 = 3015 x 2 = 30

15 x 3 = 4515 x 3 = 45

15 x 4 = 6015 x 4 = 60

15 x 5 = 7515 x 5 = 75

15 x 6 = 9015 x 6 = 90

15 x 7 = 10515 x 7 = 105

15 x 8 = 12015 x 8 = 120


Therefore…to express Therefore…to express the first 8 multiples of the first 8 multiples of 15, your answer would 15, your answer would look like:look like:


Example 6Example 6:: Find the first 8 multiples of Find the first 8 multiples of 15.15.

15 x 1 = 1515 x 1 = 15

15 x 2 = 3015 x 2 = 30

15 x 3 = 4515 x 3 = 45

15 x 4 = 6015 x 4 = 60

15 x 5 = 7515 x 5 = 75

15 x 6 = 9015 x 6 = 90

15 x 7 = 10515 x 7 = 105

15 x 8 = 12015 x 8 = 120


1515: 15, 30, 45, 60, : 15, 30, 45, 60, 75, 90, 105, 120 75, 90, 105, 120 ……

Therefore…to express Therefore…to express the first 8 multiples of the first 8 multiples of 15, your answer would 15, your answer would look like:look like:

Guided Practice ProblemsGuided Practice ProblemsDirectionsDirections:: Find all the factors of each Find all the factors of each

number and identify as prime or number and identify as prime or composite.composite.

1. 251. 25

2. 1002. 100

3. 493. 49

4. 234. 23


Guided Practice ProblemsGuided Practice Problems

DirectionsDirections:: Find all the factors of each Find all the factors of each number and identify as prime or number and identify as prime or composite.composite.

1. 251. 25 => => 2525: 1, 5, 25 (composite): 1, 5, 25 (composite)

2. 1002. 100 => => 100100: 1, 2, 4, 5, 10, 20, 25, 50, : 1, 2, 4, 5, 10, 20, 25, 50, 100 (composite)100 (composite)

3. 493. 49 => => 4949: 1, 7, 49 (composite): 1, 7, 49 (composite)

4. 234. 23 => => 2323: 1, 23 (prime): 1, 23 (prime)


Independent Practice ProblemsIndependent Practice ProblemsDirectionsDirections:: Find all the factors of each Find all the factors of each

number and identify as prime or number and identify as prime or composite.composite.

1. 361. 36

2. 372. 37

3. 423. 42

4. 804. 80


Independent Practice ProblemsIndependent Practice Problems

DirectionsDirections:: Find all the factors of each number Find all the factors of each number and identify as prime or composite.and identify as prime or composite.

1. 361. 36 => => 3636: 1, 2, 3, 4, 6, 9, 12, 36 : 1, 2, 3, 4, 6, 9, 12, 36 (composite)(composite)

2. 372. 37 => => 3737: 1, 37 (prime): 1, 37 (prime)

3. 423. 42 => => 4242: 1, 2, 3, 6, 7, 14, 21, 42 : 1, 2, 3, 6, 7, 14, 21, 42 (composite)(composite)

4. 804. 80 => => 2323: 1, 2, 4, 5, 8, 10, 16, 20, 40, 80 : 1, 2, 4, 5, 8, 10, 16, 20, 40, 80 (composite)(composite)


Guided & Independent Practice Guided & Independent Practice ProblemsProblems

DirectionsDirections:: Find the first 4 multiples of Find the first 4 multiples of each number.each number.

1. 51. 5

2. 92. 9

3. 163. 16

4. 1204. 120


Guided & Independent Practice Guided & Independent Practice ProblemsProblems

DirectionsDirections:: Find the first 4 multiples of Find the first 4 multiples of each number.each number.

1. 51. 5 => => 55: 5, 10, 15, 20,…: 5, 10, 15, 20,…

2. 92. 9 => => 99: 9, 18, 27, 36,…: 9, 18, 27, 36,…

3. 163. 16 => => 1616: 16, 32, 48, 64,…: 16, 32, 48, 64,…

4. 1204. 120 => => 120120: 120, 240, 360, 480,…: 120, 240, 360, 480,…


Homework

p.158 #1-4, 9-12, all


factors & multiples. essential question: how can we determine if a number is prime or composite?...

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