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7-1 Factors and Greatest Common Factors
Objectives
Write the prime factorization of
numbers.
Find the GCF of monomials.
Holt McDougal Algebra 1
7-1 Factors and Greatest Common Factors
Vocabulary
prime factorization
greatest common factor
Holt McDougal Algebra 1
7-1 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 McDougal Algebra 1
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7-1 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 McDougal Algebra 1
7-1 Factors and Greatest Common Factors
Example 1: Writing Prime Factorizations
Write the prime factorization of 98.
Method 1 Factor tree
Method 2 Ladder diagram
Choose any two factors
Choose a prime factor of 98
of 98 to begin. Keep finding
to begin. Keep dividing by
factors until each branch
prime factors until the
ends in a prime factor.
quotient is 1.
98
2 98
7 49
2  49
7 7
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7
7
1
98 = 2  7  7
98 = 2  7  7
The prime factorization of 98 is 2  7  7 or 2  72.
Holt McDougal Algebra 1
7-1 Factors and Greatest Common Factors
Check It Out! Example 1
Write the prime factorization of each number.
a. 40
40
2  20
2  10
2  5
40 = 23  5
The prime factorization
of 40 is 2  2  2  5 or
23  5.
Holt McDougal Algebra 1
b. 33
11 33
3
33 = 3  11
The prime factorization
of 33 is 3  11.
7-1 Factors and Greatest Common Factors
Check It Out! Example 1
Write the prime factorization of each number.
c. 49
d. 19
49
7  7
49 = 7  7
The prime factorization
of 49 is 7  7 or 72.
Holt McDougal Algebra 1
1 19
19
19 = 1  19
The prime factorization
of 19 is 1  19.
7-1 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 McDougal Algebra 1
7-1 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.
factors of 100: 1, 2, 4,
5, 10, 20, 25, 50, 100
List all the factors.
factors of 60: 1, 2, 3, 4, 5,
6, 10, 12, 15, 20, 30, 60
Circle the GCF.
The GCF of 100 and 60 is 20.
Holt McDougal Algebra 1
7-1 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.
26 =
2  13
52 = 2  2  13
2  13 = 26
Write the prime
factorization of each
number.
Align the common
factors.
The GCF of 26 and 52 is 26.
Holt McDougal Algebra 1
7-1 Factors and Greatest Common Factors
Check It Out! Example 2a
Find the GCF of each pair of numbers.
12 and 16
Method 1 List the factors.
factors of 12: 1, 2, 3, 4, 6, 12
List all the factors.
factors of 16: 1, 2, 4, 8, 16
Circle the GCF.
The GCF of 12 and 16 is 4.
Holt McDougal Algebra 1
7-1 Factors and Greatest Common Factors
Check It Out! Example 2b
Find the GCF of each pair of numbers.
15 and 25
Holt McDougal Algebra 1
7-1 Factors and Greatest Common Factors
Example 3A: Finding the GCF of Monomials
Find the GCF of each pair of monomials.
15x3 and 9x2
Holt McDougal Algebra 1
7-1 Factors and Greatest Common Factors
Example 3B: Finding the GCF of Monomials
Find the GCF of each pair of monomials.
8x2 and 7y3
Holt McDougal Algebra 1
7-1 Factors and Greatest Common Factors
Check It Out! Example 3a
Find the GCF of each pair of monomials.
18g2 and 27g3
Holt McDougal Algebra 1
7-1 Factors and Greatest Common Factors
Check It Out! Example 3b
Find the GCF of each pair of monomials.
16a6 and 9b
Holt McDougal Algebra 1
7-1 Factors and Greatest Common Factors
Check It Out! Example 3c
Find the GCF of each pair of monomials.
8x and 7v2
Holt McDougal Algebra 1
7-1 Factors and Greatest Common Factors
Lesson Quiz: Part I
Write the prime factorization of each number.
1. 50
2  52
2. 84
22  3  7
Find the GCF of each pair of numbers.
3. 18 and 75 3
4. 20 and 36 4
Holt McDougal Algebra 1
7-1 Factors and Greatest Common Factors
Lesson Quiz: Part II
Find the GCF of each pair of monomials.
5. 12x and 28x3 4x
6. 27x2 and 45x3y2 9x2
7. Cindi is planting a rectangular flower bed with 40
orange flower and 28 yellow flowers. She wants
to plant them so that each row will have the
same number of plants but of only one color. How
many rows will Cindi need if she puts the greatest
possible number of plants in each row?
17
Holt McDougal Algebra 1