Chapter 9.1
FACTORING A NUMBER
Factoring a number
 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
Factoring a number
 Prime 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)
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
Factoring a number
 Label the following as prime or composite
 24
 23
 18
 9
 53
Factoring a number
 Label the following as prime or composite
 24 Composite
 23
Prime
 18
Composite
 9
Composite
Prime
 53
Factoring a number
 Example 1: Find the prime factorization of 90
 The smallest prime
number is 2, so we
start with 2
 When you take a 2
out, you’re left with
45
Factoring a number
 Example 1: Find the prime factorization of 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
x
= 90
Factoring a number
 Example 1: Find the prime factorization of 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
x
= 45
Factoring a number
 Example 1: Find the prime factorization of 90
 15 can be factored by
3 again
 At this point, all the
number are prime
Factoring a number
 Example 1: Find the prime factorization of 90
 We can multiply all
these numbers
together to get 90
Factoring a number
 Example 1: Find the prime factorization of 90
 We can then write
3 * 3 as 32
 We now have 90 fully
factored
Factoring a number
 Example 2: Factor -28
 If it’s negative, factor
out -1 first
 Now factor a positive
28
Factoring a number
 Factor the following numbers:
1. 24
2. 36
3. -110
4. 168
5. 210
Factoring a number
 Factor the following numbers:
1. 24
23 * 3
2. 36
22 * 32
3. -110
-1 * 2 * 5 * 11
4. 168
23 * 3 * 7
5. 210
2*3*5*7
Factoring a number
 Example 3: Factor
 Factor the
number first
Factoring a number
 Example 3: Factor
 Then factor the
variable
 Remember, x3 is
x*x*x
Factoring a number
 Example 3: Factor
 We can now reduce this to get our answer
Factoring a number
 Factor the following:
1. 20x2
2. 32x5
3. -120x3
4. 68x3y5
5. 252x4y2
Factoring a number
 Factor the following:
1. 20x2
22 * 5 * x2
2. 32x5
25 * x5
3. -120x3
4. 68x3y5
-1 * 23 * 3 * 5 * x3
22 * 17 * x3 * y5
5. 252x4y2
22 * 33 * 7 * x4 *y2
Factoring a number
 Example 4:Find the
Greatest Common
Factor of :
 We need to factor both
numbers first
and
Factoring a number
 Factor 24
Factoring a number
 Factor 36
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
Factoring a number
 Find the GCF for:
and
 Factor each number first
 Find what they have in common
Factoring a number
 Find the GCF for:
and
 Factor each number first
 Find what they have in common
Factoring a number
 Find the GCF for:
and
 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
Factoring a number
 Find the Greatest Common Factor for the
following:
1. 12 and 16
3.
54x3
and
90x5
5. 312x5 and 468x7
2. 120 and 180
4. 52x4 and 104x4
Factoring a number
 Find the Greatest Common Factor for the
following:
1. 12 and 16
4
3. 54x3 and 90x5
18x3
5. 312x5 and 468x7
156x5
2. 120 and 180
60
4. 52x4 and 104x4
26x4
Factoring a number
 Example: Find the GCF for the following
numbers:
 First, factor out each
number
Factoring a number
 Find what they have in common
 They all have one 2
 They also have one 3
Factoring a number
 Multiply the numbers
 Find the smallest value of x
and plug it in
Factoring a number
 Example: Find the GCF for the following
numbers:
 The answer is:
Factoring a number
 Factor: 252
 Factor: -594x2y4
 Find the greatest common factor:
 48 and 120
 84x5 and 112x3
 117x7, 468x4 and 351x5
Factoring a number
 Factor: 252 22*32*7
 Factor: -594x2y4 -1*2*33*11*x2*y4
 Find the greatest common factor:
 48 and 120 24
 84x5 and 112x3 28x3
 117x7, 468x4 and 351x5
117x4