LESSON #6 Prime and Composite Numbers

PRIME NUMBERS & FACTORS  PRIME NUMBER: a number that only has 2 factors (1 and itself)  FACTOR: any of the numbers that multiply to form a product = 1 X is PRIME because it has no other factors but 1 and itself

COMPOSITE NUMBERS  A number that has more than 2 factors 4: 1 X 4, 2 X 2 (factors of 4 are 1, 2, 4) 12: 1 X 12, 2 X 6, 3 X 4 (factors of 12 are 1, 2, 3, 4, 6, 12)

1: only has 1 factor (1) neither prime nor composite 0: composite because it has infinite factors (0 x 0, 0 x 1, 0 x 2…) List all the prime numbers between 0 and 20 - numbers that only has 2 factors (1 and itself) REMEMBER:

DID YOU NOTICE?  2 is the only even prime number!  Why is that?

THE FACTOR TREE (PRIME FACTORS) All natural numbers can be written as the product of prime numbers – this is called PRIME FACTORIZATION Ex: Write 48, 120 and 168 as the product of prime factors (make a factor tree) Factor trees break the number down until all factors left over are PRIME numbers!

48 6 x 8 2 x 3 2 x 4 2 x 2 6 is not prime It can be broken down 2 and 3 are prime, so we can stop here 8 is not prime It can be broken down So can 4 Now every non-prime number has been broken down into prime factors What’s left over? 2 x 3 x 2 x 2 x 2 let’s multiply that out! IT EQUALS 48!

FACTOR TREE FOR 120

FACTOR TREE FOR X 2 X 2 X 3 X 7 = 168

USING EXPONENTS FACTOR TREES  When the prime factors of a number are listed, you can use exponents to simplify them:  Prime factors of 48 = 2 x 3 x 2 x 2 x 2  There are four 2’s in this expression  That’s the same as 2 4  So the prime factors can be re-written as: 2 4 x 3

RE-WRITE THESE PRIME FACTORS USING EXPONENTS: = 2 x 2 x 2 x 3 x = 2 X 2 X 2 X 3 X = 2 3 x 3 x = 2 3 x 3 x 7

FOR YOUR NOTECARD: PRIME NUMBERS & FACTOR TREES Prime numbers only have 2 factors (1 and itself) Factor trees are done by breaking numbers down to their prime factors: 42 can be written as 6 x 7 7 is already prime so it stays as is 6 is not prime but can be written as 2 x 3 (both prime) What’s left? 2 x 3 x 7 Which equals 42 (the number we started with) If a number repeats in a list of prime factors, re-write it using exponents: 48 = 2 x 3 x 2 x 2 x 2 or 48 = 2 4 x 3

HOMEWORK  p. 22 #1  p. 23 #2 and 3  Prime Factorization Stencil