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2-6 Prime Factorization
Warm Up
Write each number as a product of two whole
numbers in as many ways as possible.
1. 6
1 · 6, 2 · 3
2. 16
1 · 16, 2 · 8, 4 · 4
3. 17
1 · 17
4. 36
1 · 36, 2 · 18, 3 · 12, 4 · 9, 6 · 6
Course 2
2-6 Prime Factorization
Learn to find the prime factorizations of
composite numbers.
Course 2
2-6 Prime
Insert Factorization
Lesson Title Here
Vocabulary
prime number
composite number
prime factorization
Course 2
2-6 Prime Factorization
A prime number is a whole number greater
than 1 that has exactly two factors, 1 and itself.
Three is a prime number because its only
factors are 1 and 3.
The first prime number is 2
The first several prime numbers are:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29
Course 2
2-6 Prime Factorization
A composite number is a whole number that
has more than two factors. Six is a composite
number because it has more than two
factors—1, 2, 3, and 6.
The number 1 has exactly one factor and
is neither prime nor composite.
Course 2
2-6 Prime Factorization
Additional Example 1: Identifying Prime and
Composite Numbers
Tell whether each number is prime or composite.
A. 11
Course 2
B. 16
The factors of 11 are
1 and 11.
The factors of 16 are
1, 2, 4, 8, and 16.
11 is prime.
16 is composite.
2-6 Prime Factorization
Check It Out: Example 1
Tell whether each number is prime or composite.
A. 14
Course 2
B. 7
The factors of 14 are
1, 2, 7, and 14.
The factors of 7 are 1
and 7.
14 is composite.
7 is prime.
2-6 Prime Factorization
A composite number can be written as the
product of its prime factors. This is called the
prime factorization of the number.
You can use a factor tree to find the prime
factors of a composite number.
Course 2
2-6 Prime Factorization
Writing Math
You can write prime factorization by using
exponents. The exponent tells how many times
to use the base as a factor.
Course 2
2-6 Prime Factorization
Additional Example 2A: Using a Factor Tree to Find
Prime Factorization
Write the prime factorization of each number.
24
24
8 · 3
4 · 2
Write 24 as the product of
two factors.
Continue factoring until all
factors are prime.
2 · 2
The prime factorization of 24 is 2 · 2 · 2 · 3
or 23 · 3.
Course 2
2-6 Prime Factorization
Additional Example 2B: Using a Factor Tree to Find
Prime Factorization
Write the prime factorization of each number.
150
150
30 · 5
10 · 3 · 5
2 · 5 · 3 · 5
Write 150 as the product
of two factors.
Continue factoring until
all factors are prime.
The prime factorization of 150 is 2 · 3 · 5 · 5, or
2 · 3 · 52.
Course 2
2-6 Insert
Lesson Title Here
Prime Factorization
Check It Out: Example 2A
Write the prime factorization of each number.
36
36
18 · 2
9 · 2 · 2
Write 36 as the product of
two factors.
Continue factoring until all
factors are prime.
3 · 3 · 2 · 2
The prime factorization of 36 is 2 · 2 · 3 · 3 or
22 · 32.
Course 2
2-6 Insert
Lesson Title Here
Prime Factorization
Check It Out: Example 2B
Write the prime factorization of the number.
90
90
45 · 2
9 · 5 · 2
3 · 3 · 5 · 2
Write 90 as the product
of two factors.
Continue factoring until
all factors are prime.
The prime factorization of 90 is 3 · 3 · 5 · 2, or
2 · 32 · 5.
Course 2
2-6 Prime Factorization
You can also use a step diagram to find
the prime factorization of a number. At
each step, divide by the smallest
possible prime number. Continue
dividing until the quotient is 1.
Course 2
2-6 Prime Factorization
Additional Example 3A: Using a Step Diagram to Find
Prime Factorization
Write the prime factorization of each number.
476
2 476
2 238
7 119
17 17
1
Divide 476 by 2. Write the
quotient below 476.
Keep dividing by a prime
number.
Stop when the quotient is 1.
The prime factorization of 476 is 2 · 2 · 7 · 17, or
22 · 7 · 17.
Course 2
2-6 Prime Factorization
Additional Example 3B: Using a Step Diagram to Find
Prime Factorization
Write the prime factorization of the number.
275
5 275
5 55
11 11
1
Divide 275 by 5. Write the quotient
below 275.
Stop when the quotient is 1.
The prime factorization of 275 is 5 · 5 · 11, or
52 · 11.
Course 2
2-6 Insert
Lesson Title Here
Prime Factorization
Check It Out: Example 3A
Write the prime factorization of each number.
324
2 324
2 162
3 81
3 27
3 9
3 3
1
The prime factorization
22 · 34.
Course 2
Divide 324 by 2. Write the
quotient below 324.
Keep dividing by a prime
number.
Stop when the quotient is 1.
of 324 is 2 · 2 · 3 · 3 · 3 · 3, or
2-6 Insert
Lesson Title Here
Prime Factorization
Check It Out: Example 3B
Write the prime factorization of the number.
325
5 325
5 65
13 13
1
Divide 325 by 5. Write the quotient
below 325.
Stop when the quotient is 1.
The prime factorization of 325 is 5 · 5 · 13, or
52 · 13.
Course 2
2-6 Prime
Insert Factorization
Lesson Title Here
Lesson Quiz: Part I
Tell whether each number is prime or composite.
Course 2
1. 23
prime
2. 39
composite
3. 27
composite
2-6 Prime
Insert Factorization
Lesson Title Here
Lesson Quiz: Part II
Write the prime factorization of each number.
4. 27
33
5. 36
2 2 · 32
6. 28
22 · 7
7. 132
22 · 3 · 11
8. 52
22 · 13
22 · 33
9. 108
Course 2