Download Chap 9-1 PP - Archbold Area Schools

Example 1
Classify Numbers as Prime
or Composite
Definitions
Factor - One of two numbers multiplied to obtain
a product. 2 x 3 = 6 thus, 2 & 3 are factors of 6
Prime Number - A whole number, greater than 1,
whose only factors are 1 and itself. The only
even prime number is 2.
Composite Number - A whole number, greater
than 1, that has more than two factors.
Factor 22. Then classify it as prime or composite.
To find the factors of 22, list all pairs of whole numbers
whose product is 22.
Answer: Since 22 has more than two factors, it is
a composite number. The factors of 22, in
increasing order, are 1, 2, 11, and 22.
Factor 31. Then classify it as prime or composite.
The only whole numbers that can be multiplied together
to get 31 are 1 and 31.
Answer: The factors of 31 are 1 and 31. Since the
only factors of 31 are 1 and itself, 31 is a
prime number.
Factor each number. Then classify it as prime
or composite.
a. 17
Answer: 1, 17; prime
b. 25
Answer: 1, 5, 25; composite
Example 2
Prime Factorization of a Positive Integer
Find the prime factorization of 84.
Use a factor tree.
84
21
3
4
7
2
2
and
All of the factors in the last branch of the factor tree
are prime.
Answer: Thus, the prime factorization of 84 is
or
Find the prime factorization of 60.
60
15
3
60 = 15 * 4
4
5
2
2
15 = 3 * 5
and
All of the factors in the last branch of the factor tree
are prime.
Answer: Thus, the prime factorization of 60 is 2*2*3*5
or 22*3*5
Example 3
Prime Factorization of a Negative Integer
Definitions
Prime Factorization - When a whole
number is expressed as the product
of factors that are all prime numbers.
Find the prime factorization of –132.
-132
-1
132
4
2
33
2
3
11
Answer: The prime factorization of –132 is
or
Find the prime factorization of –154.
Answer:
Example 4
Prime Factorization of a Monomial
Definition
Prime factorization of a constant (just
a number) can have exponents
greater than 1, but prime factorization
of variable values canNOT!
Factor
completely.
x3
18
2
9
3
Answer:
x
x
y3
x
y
y
y
3
in factored form is
This can also be written as 2*32*x*x*x*y*y*y
Factor
completely.
-26
-1
r
26
2
Answer:
t2
s
t
t
13
in factored form is -1*2*13*r*s*t*t
Factor each monomial completely.
a.
Answer:
b.
Answer:
Example 5
GCF of a Set of Monomials
Definitions
Greatest Common Factor (GCF)The product of the prime factors that
are common to two or more integers.
Find the GCF of 12 and 18.
Factor each number.
Circle the common prime factors.
The integers 12 and 18 have one 2 and one 3 as
common prime factors. The product of these common
prime factors,
or 6, is the GCF.
Answer: The GCF of 12 and 18 is 6.
.
Find the GCF of
Factor each number.
Circle the common prime factors.
Answer: The GCF of
and
is
.
Find the GCF of each set of monomials.
a. 15 and 35
Answer: 5
b.
Answer:
and
Example 6
Use Factors
Crafts Rene has crocheted 32 squares for an afghan.
Each square is 1 foot square. She is not sure how she
will arrange the squares but does know it will be
rectangular and have a ribbon trim. What is the
maximum amount of ribbon she might need to finish
an afghan?
Find the factors of 32 and draw rectangles with each
length and width. Then find each perimeter.
The factors of 32 are 1, 2, 4, 8, 16, 32.
The greatest perimeter is 66 feet. The afghan with this
perimeter has a length of 32 feet and a width of 1 foot.
Answer: The maximum amount of ribbon Rene will need
is 66 feet.
Mary wants to plant a rectangular
flower bed in her front yard with a
stone border. The area of the flower
bed will be 45 square feet and the
stones are one foot square each. What
is the maximum number of stones that
Mary will need to go around all four
sides of the flower bed?
Find the factors of 45 and draw rectangles with each
length and width. Then find each perimeter.
The factors of 45 are 1, 3, 5, 9, 15, 45.
The greatest perimeter is 92 feet. The flower bed with this
perimeter has a length of 45 feet and a width of 1 foot.
Answer: The maximum amount of stones Mary will need
is 92 feet.
Thank you for participating in
today’s lesson.
Here is your reward:
Homework:
Pages 477-478 20-60 even