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Warm­Up
Simplify
1. 5(7)
2. 12÷4
3. |2|
Solve for x:
4. 5x=15
5. 6=2+2x
1
1
1. 5(7)
2
2
2. 12÷4
3
3
3. |2|
4
4
4. 5x=15
5
5
5. 6=2+2x
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4.1 Factors and Prime Factorization
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What is factoring?
Factoring a number: Breaking down a number into smaller
numbers, that can be multiplied together to get the original
number.
Key Question: What can I multiply together to get that number?
or What can I divide that number by and get a whole number?
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Prime Numbers: A whole number greater than
1 that has exactly two whole number factors, 1
and itself.
Common Prime Numbers:
9
10
Composite Number: A whole number greater than 1
that has more than two whole number factors.
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Prime Factorization: When you write a number as a
product of prime numbers.
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Factor Tree: Diagram used to write the prime
factorization of a number
12
2
6
1
x
2
Last Row MUST
be all PRIME!
3
x
2
x 2
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Monomial: A number, a variable, or the product of
a number and one or more variables raised to
whole number powers.
CANNOT have an addition or subtraction sign!!!
ex.
4
97bnhdsf
52
x
xy
5x
8x2
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Interesting Facts:
The numbers 0 and 1 are neither prime nor composite because....
1 has only 1 factor ‐ itself
0 has an endless number of factors.
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Example 1: Factoring a number
A rectangle has an area of 18 square feet. Find all possible whole number
dimensions of a rectangle.
What is the area of a rectangle?
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Note: Whenever you factor a
number, that number and 1 will
ALWAYS be factors!!
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Checkpoint!!
Find the factors of:
1. 24
2. 48
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Factor Trees:
1st Row: # you are factoring
2nd Row: What multiplies
together to get the number
in the first row?
3rd Row ... Continue the
process until you get all
prime numbers!!
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Things to remember:
1. Your tree should end with all PRIME numbers.
2. When asked to list out the prime factors you MUST list ALL
numbers that are at the end of a branch. If it is repeated repeat it
(or write exponentially)! Your prime factors should multiply to get
your original number.
3. Everyone could do a factor tree in this class and they
be different AND RIGHT!
could ALL
4. Every number in the tree is a factor of the original number!
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Example 2: Use a factor tree to factor 10.
What is the prime factorization of 10?
What are all the factors of 10?
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Example 3: Use a factor tree to factor 16.
What is the prime factorization of 16?
What are all the factors of 16?
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Checkpoint
Use a factor tree to factor 18.
What is the prime factorization of 18?
What are all the factors of 18?
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Use a factor tree to factor 23.
What is the prime factorization of 23?
What are all the factors of 23?
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25
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Factor Tree Sheet!
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Prime vs. Composite:
To determine if a number is prime or composite try to make a factor tree.
If you find any factors that are not just the number itself and 1 then the
number is composite.
Interesting facts:
___ is the only even prime number
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Ex. Is 23 prime?
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Ex. Is 21 prime?
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Checkpoint Determine if the numbers are prime or composite:
1.
33
2. 19
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Factoring a monomial:
1. Think of coefficients (numbers) separate than variables, and think
of all the different variables separately.
2. Use prime factorization to factor the coefficient.
3. If necessary expand the variable(s) to eliminate their exponent(s).
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Example 4:
Factor: 4x2
What is the coefficient?
What is it's prime factorization?
What is the variable?
Does it have an exponent? If so, write it without an exponent.
The monomial 4x2 factored is:
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Example:
Factor the monomial: 27xy2
Prime factorization of 27:
Factor the variables:
x
Y2
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Checkpoint:
Factor the monomial:
21n5
1.
2. 18x2y3
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