Transcript Prime & Composite Numbers

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