Warm UpWarm Up

#1. We have 22 students in this class, how #1. We have 22 students in this class, how many ways could Ms. Fraser group many ways could Ms. Fraser group everyone so that all the groups are equal? everyone so that all the groups are equal?

What if we had one more student? What if What if we had one more student? What if we had one less?we had one less?

#2. A large restaurant can seat 164 people, #2. A large restaurant can seat 164 people, how could they be seated so that each how could they be seated so that each table has the same number of people? table has the same number of people?

Warm Up September 8Warm Up September 8 Take out a sheet of looseleafTake out a sheet of looseleaf Number warm up is your title Number warm up is your title Number from 1-8Number from 1-8

Mil. Hun. Thou Ten Thou Thousands Hundreds Tens Ones

PRIME AND COMPOSITE PRIME AND COMPOSITE NUMBERSNUMBERS

LESSON 2LESSON 2

PRIME NUMBERSPRIME NUMBERS

A A Prime NumberPrime Number can be divided evenly can be divided evenly only by 1, or itselfonly by 1, or itself..

EXAMPLES:EXAMPLES: 2,3,5,7,11,13,17,19,23,29,31,37,41,43,472,3,5,7,11,13,17,19,23,29,31,37,41,43,47

COMPOSITE NUMBERSCOMPOSITE NUMBERS

A A Composite NumberComposite Number can be divided can be divided evenly by numbersevenly by numbers other than 1 or itself.other than 1 or itself.

EXAMPLES:EXAMPLES: 4,6,8,9,10,12,14,15,16,18,20,21,22,24,25,4,6,8,9,10,12,14,15,16,18,20,21,22,24,25,

26,27,28,30,32,33,34,35,36,38,39,4026,27,28,30,32,33,34,35,36,38,39,40

FACTORS FACTORS

A number may be made by multiplying two A number may be made by multiplying two or more other numbers together.or more other numbers together.

The numbers that are multiplied together The numbers that are multiplied together are called factors.are called factors.

EXAMPLE:EXAMPLE:

FACTORS FACTORS

A number may be made by multiplying two A number may be made by multiplying two or more other numbers together.or more other numbers together.

The numbers that are multiplied together The numbers that are multiplied together are called factors.are called factors.

EXAMPLE:EXAMPLE:• 3 X 4 = 123 X 4 = 12

FACTOR FACTOR

PRODUCT

FACTORSFACTORS

Therefore PRIME numbers have 2 factors: Therefore PRIME numbers have 2 factors: one and itself.one and itself.

COMPOSITE numbers have more than COMPOSITE numbers have more than two factors.two factors.

The number ONE only has one factor (1), The number ONE only has one factor (1), therefore it is not prime nor composite but therefore it is not prime nor composite but SPECIAL.SPECIAL.

Try theseTry these

Is the number prime or composite?Is the number prime or composite?

a) 9a) 9 b) 7b) 7 c) 23c) 23 d) 24d) 24

e) 57e) 57 f) 144f) 144

List all of the factors of the composite List all of the factors of the composite numbersnumbers

GCFGCF

GCF – GREATEST COMMON FACTORGCF – GREATEST COMMON FACTOR

The GCF is the highest factor that two or The GCF is the highest factor that two or more numbers have in common.more numbers have in common.

EXAMPLE:EXAMPLE: The factors of 18 are {1,2,3,6,9,18}The factors of 18 are {1,2,3,6,9,18} The factors of 24 are {1,2,3,4,6,8,12,24}The factors of 24 are {1,2,3,4,6,8,12,24}

GCFGCF

GCF – GREATEST COMMON FACTORGCF – GREATEST COMMON FACTOR

The GCF is the highest factor that two or more The GCF is the highest factor that two or more numbers have in common.numbers have in common.

EXAMPLE:EXAMPLE: The factors of 18 are {1,2,3,The factors of 18 are {1,2,3,66,9,18},9,18} The factors of 24 are {1,2,3,4,The factors of 24 are {1,2,3,4,66,8,12,24},8,12,24} The GCF is The GCF is 6.6.

Try theseTry these

Find the Greatest Common Factor. ( GCF)Find the Greatest Common Factor. ( GCF)

a) 28, 49a) 28, 49 b) 32, 48b) 32, 48 c) 24, 36c) 24, 36

PRIME FACTORSPRIME FACTORS

Factors that are prime numbers.Factors that are prime numbers.

When a composite number is written as a When a composite number is written as a product of all of its prime factors, we have the product of all of its prime factors, we have the prime factorization of the number.prime factorization of the number.

EXAMPLE: the number 72 can be written as a EXAMPLE: the number 72 can be written as a product of primes as: 72 =product of primes as: 72 =2x2x2x3x3 2x2x2x3x3 ..

The expression "The expression "2x2x2x3x32x2x2x3x3" is said to be the " is said to be the prime factorizationprime factorization of 72. of 72.

TRY THIS ONETRY THIS ONE

Find the PRIME factors of 32Find the PRIME factors of 32

SOLUTION:SOLUTION:

TRY THIS ONETRY THIS ONE

Find the PRIME factors of 32Find the PRIME factors of 32

SOLUTION:SOLUTION: 32

4 x 8

2 x 2 x 2 x 2 x 2

= 25

Try theseTry these

Express the number as a product of its Express the number as a product of its prime factors.prime factors.

a)a) 4242

LCMLCM

LCM – LOWEST COMMON MULTIPLELCM – LOWEST COMMON MULTIPLE

A A common multiplecommon multiple is a number that is a is a number that is a multiple of two or more numbers. multiple of two or more numbers.

The common multiples of 3 and 4 are:The common multiples of 3 and 4 are: 0, 12, 24,….0, 12, 24,….

LCMLCM

The The least common multipleleast common multiple (LCM) of two (LCM) of two numbers is the smallest number (not zero) numbers is the smallest number (not zero) that is a multiple of both.that is a multiple of both.

EXAMPLE:EXAMPLE: Multiples of 3: 6,9,12,15,18,21,24,…Multiples of 3: 6,9,12,15,18,21,24,… Multiples of 4: 8,12,16,20,24,….Multiples of 4: 8,12,16,20,24,…. LCM of 3 and 4 is: LCM of 3 and 4 is:

The The least common multipleleast common multiple (LCM) of two (LCM) of two numbers is the smallest number (not zero) numbers is the smallest number (not zero) that is a multiple of both.that is a multiple of both.

EXAMPLE:EXAMPLE: Multiples of 3: 6,9,Multiples of 3: 6,9,1212,15,18,21,24,…,15,18,21,24,… Multiples of 4: 8,Multiples of 4: 8,1212,16,20,24,….,16,20,24,…. LCM of 3 and 4 is: LCM of 3 and 4 is: 1212

Try theseTry these

Find the Lowest Common Multiple. ( LCM )Find the Lowest Common Multiple. ( LCM )

a) 18, 27a) 18, 27 b) 10, 25b) 10, 25

1. Two companies are using the telephone 1. Two companies are using the telephone book to choose winners for some book to choose winners for some promotional prizes. One company promotional prizes. One company phones every 36th name and the second phones every 36th name and the second company phones every 24th name. company phones every 24th name. What is the position of the first name that What is the position of the first name that wins both prizes?wins both prizes?