1. Chapter 9.1
Factoring a number

2. Objective NCSCOS 1.01 – Write equivalent forms of algebraic expressions to solve problems
Students will know how to factor number and find the greatest common factor

3. Vocabulary Factoring a number Prime number – Composite number –
A number that can only be divided by 1 and itself
Ex. 2, 3, 5, 7, 11, 13
Composite number –
A number that can be divided by more than 1 and itself
Ex. 4: (1*4, 2*2)
Ex. 6: (1*6, 2*3)

4. Vocabulary Factoring a number Prime Factorization –
A composite number expressed as a product of factors that are all prime numbers
The process of factoring a number down to only prime numbers

5. Factoring a number Label the following as prime or composite 24 23 189 53

6. Factoring a number Label the following as prime or composite 24 23 189 53
Composite
Prime
Composite
Composite
Prime

7. Factoring a number
Example 1: Find the prime factorization of 90 90
The smallest prime number is 2, so we start with 2
When you take a 2 out, you’re left with 45 2 45

8. Factoring a number
Example 1: Find the prime factorization of 90 90
The two numbers below 90 should multiply to the number above it
2 can’t be factored any more, so we’ll have to factor the 45 more 2 45 x
= 90

9. Factoring a number
Example 1: Find the prime factorization of 90 90
The next smallest prime number is 3, so take 3 out of 45
Notice that 3 and 15 multiply to the number above it 2 45 3 15 x
= 45

10. Factoring a number
Example 1: Find the prime factorization of 90 90
15 can be factored by 3 again
At this point, all the number are prime 2 45 3 15 3 5

11. 90 2 45 3 15 * 3 * 3 * 5 = 90 2 3 5 Factoring a number
Example 1: Find the prime factorization of 90 90
We can multiply all these numbers together to get 90 2 45 3 15
* 3
* 3
* 5
= 90 2 3 5

12. 90 2 45 3 15 * 3 * 32 * 3 * 5 = 90 2 3 5 Factoring a number
Example 1: Find the prime factorization of 90 90
We can then write * 3 as 32
We now have 90 fully factored 2 45 3 15
* 3
* 32
* 3
* 5
= 90 2 3 5

13. -28 -1 28 2 14 2 7 -1 * 22 * 2 * 2 * 7 Factoring a number
Example 2: Factor -28
If it’s negative, factor out -1 first
Now factor a positive 28 -1 28 2 14 2 7 -1
* 22
* 2
* 2
* 7

14. Factoring a number
Factor the following numbers:
1. 24
2. 36
4. 168
5. 210

15. Factoring a number
Factor the following numbers:
1. 24
2. 36
23 * 3
22 * 32
4. 168
-1 * 2 * 5 * 11
23 * 3 * 7
5. 210
2 * 3 * 5 * 7

16. 36x3 2 18x3 2 9x3 3 3x3 2 * 2 * 3 * 3x3 Factoring a number
Example 3: Factor 2
Factor the number first
18x3 2
9x3 3
3x3 2
* 2
* 3
* 3x3

17. 36x3 2 18x3 2 9x3 3 3x3 2 * 2 * 3 * 3 * 3x3 *x*x*x Factoring a number
Example 3: Factor 2
Then factor the variable
Remember, x3 is x*x*x
18x3 2
9x3 3
3x3 2
* 2
* 3
* 3
* 3x3
*x*x*x

18. 36x3 22 * 32 * x3 2 * 2 * 3 * 3 * x * x * x Factoring a number
Example 3: Factor
We can now reduce this to get our answer
22 * 32 * x3 2
* 2
* 3
* 3
* x * x * x

19. Factoring a number 1. 20x2 2. 32x5 3. -120x3 4. 68x3y5 5. 252x4y2
Factor the following:
1. 20x2
2. 32x5 x3
4. 68x3y5
5. 252x4y2

20. Factoring a number 1. 20x2 2. 32x5 22 * 5 * x2 25 * x5 3. -120x3
Factor the following:
1. 20x2
2. 32x5
22 * 5 * x2
25 * x5 x3
4. 68x3y5
-1 * 23 * 3 * 5 * x3
22 * 17 * x3 * y5
5. 252x4y2
22 * 33 * 7 * x4 *y2

21. Factoring a number
Example 4:Find the Greatest Common Factor of : 24 36
and
We need to factor both numbers first

22. Factoring a number 24
Factor 24 2 12 2 6 2 3

23. Factoring a number 36
Factor 36 2 18 9 2 3 3

24. Factoring a number
Write out each numbers factors
Find what they have in common
Multiply what they have in common to find the Greatest Common Factor GCF
24 = 2
* 2
* 2
* 3
36 = 2
* 2
* 3
* 3
2 * 2 * 3 = 12

25. 28x3 42x5 28x3 = 2*2*7*x*x*x 42x5 = 2*3*7*x*x*x*x*x GCF = 2*7*x*x*x
Factoring a number
28x3
42x5
Find the GCF for:
Factor each number first
Find what they have in common
and
28x3 = 2*2*7*x*x*x
42x5 = 2*3*7*x*x*x*x*x
GCF = 2*7*x*x*x
= 2*7*x3

26. 28x3 42x5 28x3 = 2*2*7*x*x*x 42x5 = 2*3*7*x*x*x*x*x GCF = 2*7*x3
Factoring a number
28x3
42x5
Find the GCF for:
Factor each number first
Find what they have in common
and
28x3 = 2*2*7*x*x*x
42x5 = 2*3*7*x*x*x*x*x
GCF = 2*7*x3
= 14x3

27. 28x3 42x5 GCF = 14x3 Factoring a number and Find the GCF for:
You have to factor the numbers to find the GCF but you can use a shortcut for the variables:
Which value of x has the lowest number as an exponent will be your GCF
and
GCF = 14x3

28. Factoring a number 1. 12 and 16 2. 120 and 180 4. 52x4 and 104x4
Find the Greatest Common Factor for the following:
and 16
and 180
4. 52x4 and 104x4
3. 54x3 and 90x5
5. 312x5 and 468x7

29. Factoring a number 1. 12 and 16 2. 120 and 180 4 60 4. 52x4 and 104x4
Find the Greatest Common Factor for the following:
and 16
and 180 4 60
4. 52x4 and 104x4
3. 54x3 and 90x5
18x3
26x4
5. 312x5 and 468x7
156x5

30. Factoring a number
Example: Find the GCF for the following numbers:
12x3
18x2
42x5
First, factor out each number
12x3 = 2 * 2 * 3 * x3
18x2 = 2 * 3 * 3 * x2
42x5 = 2 * 3 * 7 * x5

31. Factoring a number
Find what they have in common
They all have one 2
They also have one 3
* 3 2
12x3 = 2 * 2 * 3 * x3
18x2 = 2 * 3 * 3 * x2
42x5 = 2 * 3 * 7 * x5

32. Factoring a number
Multiply the numbers
Find the smallest value of x and plug it in
* 3 2
= 6 x2
12x3 = 2 * 2 * 3 * x3
18x2 = 2 * 3 * 3 * x2
42x5 = 2 * 3 * 7 * x5

33. Quiz! 12x3 18x2 42x5 6x2 Factoring a number
Example: Find the GCF for the following numbers:
Quiz!
12x3
18x2
42x5
6x2
The answer is:

34. Quiz! Factoring a number Factor: 252 Factor: -594x2y4
Find the greatest common factor:
48 and 120
84x5 and 112x3
117x7, 468x4 and 351x5

35. Quiz! Factoring a number Factor: 252 Factor: -594x2y4
Find the greatest common factor:
48 and 120
84x5 and 112x3
117x7, 468x4 and 351x5
22*32*7
-1*2*33*11*x2*y4 24
28x3
117x4