Download NS 1.2- Prime Factors.notebook

NS 1.2­ Prime Factors.notebook
September 11, 2015
Prime Factors
Today's lesson relies on some skills that you have been taught in previous years (mostly in Grade 7). Last year, you learned how to find factors of numbers (breaking a larger number down into two numbers that can be multiplied together to give you the original number)
*All numbers, except 1, can be written as the product of two different factors
Example: 2 and 4 are factors of 8 because 2 x 4 = 8 1 and 8 are also factors of 8 because 1 x 8 = 8
Some numbers have lots of factors. For example, see if you can find all the factors of 24.
*Any number than has more than 2 factors is called a composite number
*Any number that ONLY has 2 factors is said to be a prime number. If a number only has two factors, those factors will always be itself and 1.
NS 1.2­ Prime Factors.notebook
September 11, 2015
Let's Practice.....
Prime or Composite? Prove it!
7
123
9
32
87
NS 1.2­ Prime Factors.notebook
September 11, 2015
Some tips to remember...
*All numbers have at least 2 factors (itself and one)
*All even numbers (except 2) are composite because if a number is even, it can be
divided by 2.
Example 2346 is composite because the last digit (6) is even. 2346/2 = 1173, so 2 and
1173, 1 and 2346 are all factors of 2346
**Use guess-and-check to look for factors of numbers. You can always stop when you
reach a repeated factor or when you reach half-way to the number.
*Use division to help you with guess-and-check.
Start with the number in question and use your calculator to see which numbers
divide equally into the number.
Example: 27
1 x 27 (because 27/1= 27)
2 (because 27/2 = 13.5; you cannot make equal groups of 2 from 27)
3 x 9 (because 27/3 =9)
4
5
6
7
8
9 **I can stop here because 9 is already a factor (3 x 9)
The factors of 27 are 1, 3, 9, 27.
NS 1.2­ Prime Factors.notebook
September 11, 2015
Here's the new stuff....
In Grade 8, we take factoring to the next level by finding prime factors.
-Prime factors are prime numbers than can be multiplied together to make the
original number.
*To become efficient at finding prime factors, it is important that you know
your prime numbers (2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, etc.)
Why do we need to do this?
-Some numbers (especially some bigger ones) have LOTS of factors but all
numbers only have one set of prime factors
-Finding prime factors of numbers breaks numbers down to their simplest
form and makes it easier to compare numbers (you will see this a bit later)
-Prime factorization is a important skill that will help you with other skills
later this year and beyond
NS 1.2­ Prime Factors.notebook
September 11, 2015
How to find prime factors of numbers.
Let's start with 100 as a example.
We are going to take our number in focus and try to divide it by the least prime number (2).
*How will we know if 2 works for our number in question?
100/2 = 50, so we know that 2 is a prime factor of 100
­next, we will look at 50 to see if it can be factored further and check it with the least prime number (2) 50/2 = 25, so we know that 2 can be "taken out" of 100 a second time
­now, we check 25. 2 is not a factor of 25, so we move onto the next prime number (3)
3 is not a factor of 25, so we move on (5 is next)
25/5 = 5, so we know that 5 is a prime factor of 100
­now, we check 5 again
5/5 = 1, so we know that 5 can be "taken out" of 100 a second time
*We are done because the number that we have left is 1
2 x 2 x 5 x 5 = 100
22 x 52 = 100
NS 1.2­ Prime Factors.notebook
Ways to organize.....
September 11, 2015
NS 1.2­ Prime Factors.notebook
September 11, 2015
Let's try another one together...
Find the prime factors of 147
147/2 will not work
147/3 = 49, so 3 is a prime factor of 147
49: 2, 3, 5 will not work but 7 will (49/7 =7), so 7 is a prime factor of 147
7: 2, 3, 5 will not work but 7 will 7/7 = 1), so 7 can be "taken out" of 147 again
3 x 7 x 7 = 147
3 x 72 = 147
NS 1.2­ Prime Factors.notebook
One more to try before you go....
Find the prime factors of 194.....
September 11, 2015
NS 1.2­ Prime Factors.notebook
September 11, 2015
Homework...
*Please practise tonight because tomorrow we more forward with applications of prime factorization
Tools to help you: http://www.mathsisfun.com/prime_numbers.html