Warm Up #1. We have 22 students in this class, how many ways could Ms. Fraser group everyone so that all the groups are equal? What if we had one more student? What if we had one less? #2. A large restaurant can seat 164 people, how could they be seated so that each table has the same number of people?

Warm Up September 8  Take out a sheet of looseleaf  Number warm up is your title  Number from 1-8 Mil.Hun. ThouTen ThouThousandsHundredsTensOnes

PRIME AND COMPOSITE NUMBERS LESSON 2

PRIME NUMBERS  A Prime Number can be divided evenly only by 1, or itself.  EXAMPLES:  2,3,5,7,11,13,17,19,23,29,31,37,41,43,47

COMPOSITE NUMBERS  A Composite Number can be divided evenly by numbers other than 1 or itself.  EXAMPLES:  4,6,8,9,10,12,14,15,16,18,20,21,22,24,25, 26,27,28,30,32,33,34,35,36,38,39,40

FACTORS  A number may be made by multiplying two or more other numbers together.  The numbers that are multiplied together are called factors.  EXAMPLE:

FACTORS  A number may be made by multiplying two or more other numbers together.  The numbers that are multiplied together are called factors.  EXAMPLE: 3 X 4 = 12 3 X 4 = 12 FACTOR PRODUCT

FACTORS  Therefore PRIME numbers have 2 factors: one and itself.  COMPOSITE numbers have more than two factors.  The number ONE only has one factor (1), therefore it is not prime nor composite but SPECIAL.

Try these Is the number prime or composite? a) 9b) 7c) 23d) 24 e) 57f) 144 List all of the factors of the composite numbers

GCF  GCF – GREATEST COMMON FACTOR  The GCF is the highest factor that two or more numbers have in common.  EXAMPLE:  The factors of 18 are {1,2,3,6,9,18}  The factors of 24 are {1,2,3,4,6,8,12,24}

GCF  GCF – GREATEST COMMON FACTOR  The GCF is the highest factor that two or more numbers have in common.  EXAMPLE:  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 GCF is 6.

Try these Find the Greatest Common Factor. ( GCF) a) 28, 49b) 32, 48c) 24, 36

PRIME FACTORS  Factors that are prime numbers.  When a composite number is written as a product of all of its prime factors, we have the prime factorization of the number.  EXAMPLE: the number 72 can be written as a product of primes as: 72 =2x2x2x3x3.  The expression "2x2x2x3x3" is said to be the prime factorization of 72.

TRY THIS ONE  Find the PRIME factors of 32  SOLUTION:

TRY THIS ONE  Find the PRIME factors of 32  SOLUTION: 32 4 x 8 2 x 2 x 2 x 2 x 2 = 2 5

Try these Express the number as a product of its prime factors. a) 42

LCM  LCM – LOWEST COMMON MULTIPLE  A common multiple is a number that is a multiple of two or more numbers. common multiplecommon multiple  The common multiples of 3 and 4 are:  0, 12, 24,….

LCM  The least common multiple (LCM) of two numbers is the smallest number (not zero) that is a multiple of both. least common multipleleast common multiple  EXAMPLE:  Multiples of 3: 6,9,12,15,18,21,24,…  Multiples of 4: 8,12,16,20,24,….  LCM of 3 and 4 is:

 The least common multiple (LCM) of two numbers is the smallest number (not zero) that is a multiple of both. least common multipleleast common multiple  EXAMPLE:  Multiples of 3: 6,9,12,15,18,21,24,…  Multiples of 4: 8,12,16,20,24,….  LCM of 3 and 4 is: 12

Try these Find the Lowest Common Multiple. ( LCM ) a) 18, 27b) 10, 25

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