Transcript Factors_ Prime Factorization_ and Greatest Common H_W_ Notes

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Vocabulary
Whole numbers that are multiplied to
find a product are called factors of that
product. A number is divisible by its
factors.
2 3=6
Factors
Product
6 ÷3 = 2
6 ÷2 = 3
6 is divisible
by 3 and 2.
Example 1: Finding Factors
List all of the factors of the number 16.
A. 16
Example 2
List all of the factors of the number 12.
A. 12
Vocabulary
You can use factors to write a number
in different ways.
Factorization of 12
1 • 12
2•6
3•4
3•2•2
Notice that
these factors
are all prime.
The prime factorization of a number is
the number written as the product of its
prime factors.
Helpful Hint
You can use exponents to write prime
factorizations. Remember that an
exponent tells you how many times the
base is a factor.
Example 3: Writing Prime Factorizations
Write the prime factorization of 24.
Method 1: Use a factor tree.
Example 4: Writing Prime Factorizations
Write the prime factorization of 45.
Method 2: Use a ladder diagram.
The prime factorization of45 is 3 • 3 • 5 or 32 • 5 .
Example 5
Write the prime factorization of 28.
Method 1: Use a factor tree.
Example 6
Write the prime factorization of 36.
Method 2: Use a ladder diagram.
Vocabulary
Factors shared by two or more whole numbers
are called common factors. The largest of the
common factors is called the greatest
common factor, or GCF.
Factors of 24:
Factors of 36:
1, 2, 3, 4, 6, 8, 12, 24
1, 2, 3, 4, 6, 9, 12, 18, 36
Common factors: 1, 2, 3, 4, 6, 12
The greatest common factor (GCF) of 24 and 36
is 12.
Example 1 shows three different methods for
finding the GCF.
Example 7: Finding the GCF
Find the GCF of the set of numbers.
28 and 42
Method 1: List the factors.
Example 8: Finding the GCF
Find the GCF of the set of numbers.
18, 30, and 24
Method 2: Use the prime
factorization.
Example 9: Real-World Application
Jenna has 16 red flowers and 24 yellow
flowers. She wants to make bouquets with
the same number of each color flower in
each bouquet. What is the greatest
number of bouquets she can make?
Example 10: Real-World Application
Peter has 18 oranges and 27 pears. He
wants to make fruit baskets with the
same number of each fruit in each
basket. What is the greatest number of
fruit baskets he can make?