1. 10/16/14- SW be able to find the prime
factorization of a composite number.
What type of
number is 24?
What type of
number is 7?
2. Lesson Plan
• Rational Number Unit (includes fractions and decimals)
• Journal Notes:
– Prime Numbers
– Composite Numbers
– Prime factorization
• Two methods for prime factorization:
– Division by primes
– Factor Tree
• Factor Tree Race Group Activity
• Writing Response Questions and scale
3.
4. What is a prime?
• Prime number - a natural number greater
than 1 that has no positive divisors other
than 1 and itself.
• In other words, see what you can divide the
number by.
• If the only answers are the number itself
and one, then the number is prime.
5.
6.
7. And if it’s not prime?
If a number is not prime it is called composite.
6 is divisible by 1, 2, 3, and 6. This means that 6 is
a composite number.
A composite number is a number with three or
more factors.
8. So what is prime factorization?
• This is a way to break a number down into parts
where each part is a prime number.
• Prime factorization is a number written as a
product of it’s prime factors.
9. Let’s look at the number 6.
6 can be broken down into 3 x 2
6 3 x 2
10. • For 6 we write the prime
factorization as
• 6 = 3 x 2
11. How do we find the prime
factorization?
• Division by primes (bake a cake)
• Factor Tree (climb a tree)
12. Division by Primes
• The first method is called division by
primes (or the birthday cake
method)
• Let’s use the number 24
• First we pick a prime that we can
divide 24 by. Since it is even we will
try 2.
13. • First we divide 24 by 2 and the result is 12
• Next we choose another prime to now divide 12 by
• We divide 12 by 2 and the result is 6
• Now we choose a prime to divide 6 by, let’s choose 3 this time
• The result is 2, which is a prime, once a prime answer is reached we stop
• Now to get our answer we look on the outside of the long division
2
3 6
2 12
2 24
• The prime factorization of 24 is 2 x 2 x 2 x 3
14. The advantages to this method are in the ease of choosing your
numbers. You must choose a prime number to divide by each
time, which limits your choices to a few small numbers usually.
The reason this is sometimes called the birthday cake method is
because of the resulting shape.
2
3 6
2 12
2 24
15. Factor Tree
• The second method is called a factor tree
• Again we will use the number 24
• This time we are not limited to our choice of
numbers to divide by so we will pick 8
16. 24
8 3
4 2
2 2
• First we divide 24 by 8. The result is 3.
i.e. 8 x 3 = 24
• Next we look at 8. We can divide 8 by 4 to
get a result of 2.
• Then we look at the 3. This is a prime so we
do not touch the 3. We will circle it to indicate
we are done with it.
• The 4 can turn into 2 x 2.
• The 2 is prime so we circle it.
• The last two 2’s are prime, so again we circle
them.
• Now look at all of our circled numbers.
This is our prime factorization.
24 = 3 x 2 x 2 x 2
17. 24
8 3
4 2
2 2
• The advantage to the factor tree
method is the ability to choose
from any number. (as long you
can divide the original number
evenly)
• This method is named
for the resemblance the
final results have to a
pine tree.
19. Group activity rules
• Talk is on task
• Stay in your seats
• Polite Behavior
• Working quietly
20. 3 play
1 referee/
dice roller
(switch
positions
each game)
21. Writing Response and scale
• WR:
3, 2, 1 -
List 3 things that you learned this week
List 2 things that surprised you
List 1 question you still have (can be about
anything)
