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Objective
Find the prime factorization of a
composite number
Vocabulary
Prime number
A whole number greater than 1 that has exactly
two factors, 1 and itself
Vocabulary
Composite number
A whole number greater than 1 that has more
than 2 factors
Vocabulary
Prime factorization
Expressing a composite number as a product
of prime numbers
Vocabulary
Factor tree
A diagram showing the prime factorization of a
number
Review
Vocabulary
Factors
Two or more numbers that are multiplied
together to form a product
Example 1 Identify Numbers as Prime or Composite
Example 2 Identify Numbers as Prime or Composite
Example 3 Find the Prime Factorization
Example 4 Factor an Algebraic Expression
Determine whether the number 63 is prime or
composite.
Write the number
63
6+3=9
93=3
All numbers (except 1) has 2 factors:
1 and the number itself
Determine if any number other than
1 and 63 are factors of 63
Remember divisibility rules:
If the sum of the digits is divisible by 3
then the number is divisible by 3
63 is divisible by 3 so is not prime
Answer: Composite
1/4
Determine whether the number 41 is prime or
composite.
Answer: prime
1/4
Determine whether the number 29 is prime or composite.
Write the number
29
2 + 9 = 11
All numbers (except 1) has 2 factors:
1 and the number itself
Determine if any number other than
1 and 29 are factors of 29
Remember divisibility rules:
If the sum of the digits is divisible by 3
then the number is divisible by 3
2/4
Determine whether the number 29 is prime or composite.
Remember divisibility rules:
29
2 + 9 = 11
11 is not divisible by 3 so 29 is not
divisible by 3
29 is not even so is not divisible by 2
Continue checking divisibility by prime
numbers
The one’s digit is not a 0 or 5 so is not
divisible by 5
2/4
Determine whether the number 29 is prime or composite.
Remember divisibility rules:
29
2 + 9 = 11
29 is not divisible by 7 because
7  4 = 28
29 is not divisible by 11 because
11  3 = 33
Since we have checked divisibility past
29 we have confirmed that 29 is a
prime number
Answer: Prime
2/4
Determine whether the number 24 is prime or
composite.
Answer: composite
2/4
Find the prime factorization of 100.
Write number then use factorization ladder
2 100
2 50
5 25
5
Decide on prime number that
will go evenly into 100
Can use any prime factor like 2 or 5
Decide on prime number that
will go evenly into 50
Decide on prime number that
will go evenly into 25
5 is a prime number so you are
done prime factoring
3/4
Find the prime factorization of 100.
Write using prime numbers and
exponents
2 100
2 50
5 25
5
22 
Write the smallest prime
number that was used 2
Circle the 2’s that were used
2 two’s were used so that is the
exponent with the 2
Put the multiplication sign
3/4
Find the prime factorization of 100.
Write the next smallest prime
number which is 5
2 100
2 50
5 25
5
22  5 2
Circle the 5’s that were used
2 five's were used so that is the
exponent with the 2
All prime numbers used have been
circled so you are done!
Answer: 22  52
3/4
Find the prime factorization of 72.
Answer: 23  32
3/4
ALGEBRA Factor
Write number then use factorization ladder
3 21m2n
7 2n
7 7m
Decide on prime number that
will go evenly into 21
The prime number 3 will divide
into 21 evenly
Divide 21 by 3
Bring down m2n
Decide on prime number that
will go evenly into 7
The prime number 7 will divide
into 7 evenly
4/4
ALGEBRA Factor
3 21m2n
7 2n
7 7m
m m 2n
m mn
m
Divide 7 into 7 then use the Identity
Property to multiply 1  m2n
Since m2 = m  m, m can be a
prime variable
Divide m into m2 which will be
m
Bring down the n
Remember a variable by itself is
prime so use m as a prime
4/4
ALGEBRA Factor
3 21m2n
7 2n
7 7m
m m 2n
m mn
n
Divide m into mn which will
leave n
The variable is a prime and is
by itself so you are done prime
factoring!
Now write the answer as factors
4/4
ALGEBRA Factor
3 21m2n
7 2n
7 7m
m m 2n
m mn
n
37 
Write the smallest prime
number which is 3
Circle the 3
Since the direction say “factor”
then do not use exponents
Put the multiplication sign
Circle the next factor which is 7
and write it down
Put the multiplication sign
4/4
ALGEBRA Factor
3 21m2n
7 2n
7 7m
m m 2n
m mn
n
Answer:
37 mmn
Circle the next factor which is m
and write it down
Put the multiplication sign
Circle the next factor which is m
and write it down
Put the multiplication sign
Circle the next factor which is n
and write it down
4/4
*
ALGEBRA Factor
Answer:
4/4
Assignment
Lesson 5:1
Prime Factorization
13 - 35 All