Factors
and
Greatest
and Greatest Common Factors
8-1
8-1 Factors
Common Factors
Warm Up
Lesson Presentation
Lesson Quiz
Holt
Holt
Algebra
Algebra
11
8-1 Factors and Greatest Common Factors
Bell Quiz 8-1
Tell whether the second number is a factor
of the first number
2 pts 1.
50, 6
2 pts 3.
List the factors of 28.
±14, ±28
no
2 pts
2. 105, 7
yes
±1, ±2, ±4, ±7,
Tell whether each number is prime or
composite. If the number is composite, write
it as the product of two numbers.
10 pts
2 pts 4. 11 prime
2 pts 5. 98 composite; 49 • 2
possible
Holt Algebra 1
8-1 Factors and Greatest Common Factors
Objectives
Write the prime factorization of
numbers.
Find the GCF of monomials.
Holt Algebra 1
8-1 Factors and Greatest Common Factors
Vocabulary
prime factorization
greatest common factor
Holt Algebra 1
8-1 Factors and Greatest Common Factors
The whole numbers that are multiplied to find a
product are called factors of that product. A
number is divisible by its factors.
You can use the factors of a number to write the
number as a product. The number 12 can be
factored several ways.
Factorizations of 12
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Holt Algebra 1
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8-1 Factors and Greatest Common Factors
The order of factors does not change the product,
but there is only one example below that cannot
be factored further. The circled factorization is
the prime factorization because all the factors
are prime numbers. The prime factors can be
written in any order, and except for changes in
the order, there is only one way to write the
prime factorization of a number.
Factorizations of 12
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Holt Algebra 1
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8-1 Factors and Greatest Common Factors
Remember!
A prime number has exactly two factors, itself
and 1. The number 1 is not prime because it only
has one factor.
Holt Algebra 1
8-1 Factors and Greatest Common Factors
Example 1: Writing Prime Factorizations
Write the prime factorization of 98.
Factor tree
The prime factorization of 98 is 2 7 7 or 2 72.
Holt Algebra 1
8-1 Factors and Greatest Common Factors
Check It Out! Example 1
Write the prime factorization of each number.
a. 40
b. 33
33 = 3 11
The prime factorization
of 40 is 2 2 2 5 or
23 5.
Holt Algebra 1
The prime factorization
of 33 is 3 11.
8-1 Factors and Greatest Common Factors
Check It Out! Example 1
Write the prime factorization of each number.
c. 49
The prime factorization
of 49 is 7 7 or 72.
Holt Algebra 1
d. 19
The prime factorization
of 19 is 1 19.
8-1 Factors and Greatest Common Factors
Factors that are shared by two or more whole
numbers are called common factors. The greatest
of these common factors is called the greatest
common factor, or GCF.
Factors of 12: 1, 2, 3, 4, 6, 12
Factors of 32: 1, 2, 4, 8, 16, 32
Common factors: 1, 2, 4
The greatest of the common factors is 4.
Holt Algebra 1
8-1 Factors and Greatest Common Factors
Example 2A: Finding the GCF of Numbers
Find the GCF of each pair of numbers.
100 and 60
Method 1 List the factors.
Holt Algebra 1
8-1 Factors and Greatest Common Factors
Example 2B: Finding the GCF of Numbers
Find the GCF of each pair of numbers.
26 and 52
Method 2 Prime factorization.
Write the prime
factorization of each
number.
Align the common
factors.
Holt Algebra 1
8-1 Factors and Greatest Common Factors
Check It Out! Example 2a
Find the GCF of each pair of numbers.
12 and 16
Holt Algebra 1
8-1 Factors and Greatest Common Factors
Check It Out! Example 2b
Find the GCF of each pair of numbers.
15 and 25
Holt Algebra 1
8-1 Factors and Greatest Common Factors
You can also find the GCF of monomials that
include variables. To find the GCF of monomials,
write the prime factorization of each coefficient
and write all powers of variables as products.
Then find the product of the common factors.
Holt Algebra 1
8-1 Factors and Greatest Common Factors
Example 3A: Finding the GCF of Monomials
Find the GCF of each pair of monomials.
15x3 and 9x2
Write the prime factorization of
each coefficient and write
powers as products.
Align the common factors.
Find the product of the common
factors.
The GCF of 3x3 and 6x2 is 3x2.
Holt Algebra 1
8-1 Factors and Greatest Common Factors
Example 3B: Finding the GCF of Monomials
Find the GCF of each pair of monomials.
8x2 and 7y3
The GCF 8x2 and 7y is 1.
Holt Algebra 1
Write the prime
factorization of each
coefficient and write
powers as products.
Align the common
factors.
There are no
common factors
other than 1.
8-1 Factors and Greatest Common Factors
Helpful Hint
If two terms contain the same variable raised to
different powers, the GCF will contain that
variable raised to the lower power.
Holt Algebra 1
8-1 Factors and Greatest Common Factors
Check It Out! Example 3a
Find the GCF of each pair of monomials.
18g2 and 27g3
Write the prime factorization
of each coefficient and
write powers as products.
Align the common factors.
Find the product of the
common factors.
The GCF of 18g2 and 27g3 is 9g2.
Holt Algebra 1
8-1 Factors and Greatest Common Factors
Check It Out! Example 3b
Find the GCF of each pair of monomials.
16a6 and 9b
The GCF of 16a6 and 7b is 1.
Holt Algebra 1
Write the prime
factorization of
each coefficient
and write powers
as products.
Align the common
factors.
There are no common factors
other than 1.
8-1 Factors and Greatest Common Factors
Check It Out! Example 3c
Find the GCF of each pair of monomials.
8x and 7v2
Write the prime factorization
of each coefficient and
write powers as products.
Align the common factors.
The GCF of 8x and 7v2 is 1.
Holt Algebra 1
There are no common
factors other than 1.
8-1 Factors and Greatest Common Factors
HOMEWORK
Section
8-1 (page 527)
3, 6, 9, 12, 15, 18, 21, 24,
27, 30, 33, 36, 38, 40, 41,
42, 48, 49, 50, 51, 53, 6971
Holt Algebra 1
8-1 Factors and Greatest Common Factors
HOMEWORK
Holt Algebra 1