Prime & Composite Numbers

Fun and Games

Number Theory GONE WILD!

Factors “Fall” into Families Multiples Multiply like Rabbits!

What am I Learning Today?

Prime and Composite Numbers

How will I show that I learned it?

Compare and contrast prime and composite numbers Use divisibility rules to determine a number’s characteristics

Vocabulary

Composite number: A number that is divisible by more than two numbers.

Prime number: A number greater than one that is only divisible by one and itself.

Sieve of Eratosthenes

How it’s done: A Greek mathematician, who made several discoveries, including the system of latitude and longitude. He was the first to calculate the circumference of the Earth, as well as the distance to the sun. He invented the Leap Day. He also proposed a simple algorithm for finding prime numbers.

Step 1: Circle 2 in blue because it is prime. Now cross out all the multiples of 2 with that same color.

Step 2: Circle 3 in green because it is prime. Now cross out every third number with that same color.

Step 3: Circle 5 in red because it is prime. Now cross out all the numbers that end in 0 or 5 in that same color.

Step 4: Circle 7 in yellow because it is prime. Now cross out every seventh number with that same color.

Step 5: Circle the remaining numbers, EXCEPT for one, in purple because they are all prime.

Sieve of Eratosthenes

Paired Discussion

Turn to a partner and discuss the following:

1) How can the divisibility rules help you identify composite numbers?

2) The Sieve of Eratosthenes didn’t include the number ONE. Is it prime or composite?

3) Are prime numbers mostly odd or mostly even? Explain.

Credits

http://en.wikipedia.org/wiki/File:New_Animation_Sieve_of_Erat osthenes.gif

http://my.hrw.com

Selected slides from c1_ch04_01.ppt

http://www.knowledgerush.com/kr/encyclopedia/Eratosthenes/ Picture of Eratosthenes