8 Notes S1c2po1 Prime Composite Factors Multiples

Bethune Junior High Math 7 S1C1PO2 8 S1C2PO1 www.bethunemath.wordpress.com Prime, Composite, Factors and Multiples

Name (First & Last) Date Class/Hour

21241199.doc

7TH Objective: M07-S1C1-02. Find or use factors, multiples, or prime factorization within a set of numbers. TH 8 Objective: M08-S1C2-01. Solve problems with factors, multiples, divisibility or remainders, prime numbers, and composite numbers.

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What is the difference between a factor and a multiple? When is each used?

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How are factors and prime factorization related?

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How can remainders be expressed in an answer?

Vocabulary: Composite

Factor

Factor Tree

Factorial Notation

Multiple

Prime

Prime Factorization

Factor: Number that divides

into another number.

*use blocks (arrays) to solve Ex) 12

Ex) 20

Ex) 17

Divisible: Divides evenly into a number. Ex) 12 is divisible by Ex) 15 is divisible by Divisibility Rules: (Shortcuts)

2 3 5 6 10 Write yes or no whether each number is divisible by those numbers.

1. 120

2. 375

3. 1,234

4. 82

5. 19

2

2

2

2

2

3

3

3

3

3

5

5

5

5

5

6 10

6 10

6 10

6 10

6 10

Prime and Composite Numbers Prime Numbers: Numbers with only two factors. (1 and the number itself) Ex)

Ex)

Ex)

Ex)

Composite Numbers: Numbers with more than two factors. Ex)

Ex)

Ex)

Ex)

List all the prime numbers up to 30! 1. Which set of numbers can be described as only prime numbers?

 2, 3,9,11,13 B.  2, 3,5,7,13 A.

C.

 3,5,11,15, 21 D.  2,4,10,16, 20

2. Which set of numbers can be described as only composite numbers?

 4,10,17, 20 B.  5,10,15, 20

 2,6,15, 21 D.  4,8,12,16

A.

C.

3. Which set of numbers can be described as only prime numbers?

 3,5,7,9,11 B.  3,15, 21, 25, 27

 2, 3,17,19, 23 D.  2, 3,9,11,13

A.

C.

4. Which set of numbers can be described as only composite numbers?

 2.4,8,12,17 B.  6,15, 21, 25 A.

C.

 10,14,19, 24 D.  2,5,18, 24

The Sieve of Eratosthenes Activity Use the divisibility rules to cross off composite numbers. The remaining numbers are prime. Prime Factorization: Factor the number down to all prime numbers (factor trees). Ex) 200

1. 250

2. 64

3. 80

4. 36

Write the answer using factorial notation 1. 96

2. 128

A) 24•32 B) 25•3 3. 144

C) 22•32 D) 2•3

A) 24 B) 25 4. 120

C) 26 D) 27

A) 22•34 B) 24•32

C) 23•33 D) 24•34

A) 2•32•5 B) 2•32•52

C) 23•3•5 D) 2•3•5

Greatest Common Factor The GCF is the biggest number that will divide into two numbers evenly. In other words, it's the number that contains all the common factors. So the GCF is the product of any and all factors that two numbers share. Find the Greatest Common Factor (GCF)

1. 12 18 2. 20 25 3. 6 8

4. 30 15 1. Find the Greatest Common Factor (GCF) for the given set of numbers.

{8, 10}

A. 2

B. 40

C. 20

D. 4

2. Find the Greatest Common Factor (GCF) for the given set of numbers.

{15, 30}

A. 15

B. 3

C. 5

D. 30

3. Find the Greatest Common Factor (GCF) for the given set of numbers.

{8, 12, 20}

A. 4

B. 8

C. 24

D. 12

LEAST COMMON MULTIPLE The LCM is the smallest number that two or more numbers divide into. It will be the smallest number that contains one of every factor in these two numbers.

Find the Least Common Multiple (LCM) 1. 6 8

2. 15 10 3. 15 30 4. 21 7 1. Find the Least Common Multiple (LCM) for the given set of numbers.

{8, 10}

A. 2

B. 40

C. 20

D. 4

2. Find the Least Common Multiple (LCM) for the given set of numbers.

{15, 30}

A. 15

B. 3

C. 5

D. 30

3. Find the Least Common Multiple (LCM) for the given set of numbers.

{8, 12, 20}

A. 4

1)

D. 12

Monday Tuesday Saturday Sunday

You are planning a BBQ for 40 people. You will serve hotdogs. Each of the packages of hotdogs contains 8 hotdogs and each of the packages of buns contains 6 buns. You want to buy the minimum number of packages, so that each hotdog has a bun and there are no leftovers. How many packages must you buy?

A B C D 3)

C. 24

Greg rides his bike to the mall every third day. James rides his bike to the mall every fifth day. They see each other on the way to the mall on Monday. When is the next time they will see each other on the way to the mall?

A B C D 2)

B. 8

3 packages of hotdogs, 4 packages of buns 4 packages of hotdogs, 3 packages of buns 8 packages of hotdogs, 6 packages of buns 6 packages of hotdogs, 8 packages of buns

A florist has 56 roses, 42 carnations, and 21 daisies that she can use to create bouquets. What is the greatest number of bouquets she can make containing at least one of each flower, without having any flowers left over?

A B C D

3 bouquets 7 bouquets 14 bouquets 21 bouquets

DIRECTIONS: Four numbers are shown below. Answer the questions for the numbers by indicating a T for TRUE or an F for FALSE in the corresponding box. (5 points)

3 11)

6

7

8

Two of the numbers are prime

True/False (1 point)

12) 2 is the greatest common factor for 6 and 8

True/False (1 point)

13) The least common multiple for 3, 6, 8 is 96

True/False (1 point)

14) A factor of a number is always greater than the

True/False (1 point)

number itself

15) A multiple of a number can never be larger than the

True/False (1 point)

number itself

The Sieve of Eratosthenes (multiples) – cross off multiples of numbers so you just have prime numbers left that haven’t been crossed off.

1 11 21 31 41 51 61 71 81 91

2 12 22 32 42 52 62 72 82 92

3 13 23 33 43 53 63 73 83 93

4 14 24 34 44 54 64 74 84 94

5 15 25 35 45 55 65 75 85 95

6 16 26 36 46 56 66 76 86 96

7 17 27 37 47 57 67 77 87 97

8 18 28 38 48 58 68 78 88 98

9 19 29 39 49 59 69 79 89 99

10 20 30 40 50 60 70 80 90 100

Rectangular Arrays (factors)- Use counters or square tiles to make rectangular arrays of a given number. An array is made into rows and columns. You first read the row number then the column number. For example, the students would make all arrays for the number 12. Then have them list the factors for the number 12. Is 12 prime or composite? When they make arrays for a prime number, there will only be 2 arrays because prime numbers have only 2 factors. Buzz (multiples) Count up to 50, every time you get to a multiple of a number say “buzz” Ex: multiples of 4 1, 2, 3, buzz, 5, 6, 7, buzz, 9, 10, 11, buzz *if you miss then go back to zero

Factor Captor (factors) – You begin with a number grid (see next page). Divide your class or team table into 2 teams. Give each team a different color marker. Have team 1 choose a number and circle it on the grid. Team 1 gets the number of points for the number they choose. Let’s say they choose 28, they would get 28 points. Then someone from team 2 (using their color marker) circles the factors of 28. They only get points for the factors they circle. A variation of game would be to give the other team points for naming factors that were missed. So let’s say team 2 circles 4 and 7 (11 points). If they circle a number that is NOT a factor then their turn ends and they can’t name any more factors. They will get points for the correct factors circled. When numbers have been used, they get crossed off the grid and can’t be used again. Then team 2 circles a number and team 1 has to circle the factors. They can’t circle a number that doesn’t have a factor left on the grid. The game ends when there aren’t any more numbers with factors left. EX) Team 1 28 1, 3, 6 ,12 = 22

Team 2 4, 7 = 4 + 7 = 11 36

Factor Captor

1 3 4 6 10 16 23 32 40 50

2 3 5 7 10 17 24 33 42 51

2 3 5 7 11 18 25 34 44 52

2 3 5 8 12 19 26 35 45 54 Game 1

2 4 5 8 13 20 27 36 46 55

2 4 6 9 14 21 28 38 48 56

3 4 6 9 15 22 30 39 49 60

Factor Captor

1 2 2 2 2 2 2 3 3 3 3 3 3 4 4 4 4 5 5 5 5 6 6 7 7 8 8 9 9 10 10 11 12 13 14 15 16 18 20 21 22 24 25 26 27 28 30 32 Game 2