Transcript Section 4.3: Prime Factorization and Greatest Common Factor

Warm Ups: Write in Exponential
Notation
 c•b•4•b•b=
 -5 • x • x • 3 • y • y =
 d cubed =
Warm Ups: Simplify or Evaluate
• 15 + (4+6)2  5 =
• (4 + 8)2  42 =
• -32 + 5  23 =
Section 4.3: Prime Factorization
and Greatest Common Factor
By Ms. Dewey-Hoffman
October 14th, (Tuesday)
Finding Prime Factorizations
• A PRIME NUMBER is a positive
integer, greater than 1, with
exactly two factors. 1 and itself.
• 3, 5, 7, and 9 are examples of
prime numbers.
• A COMPOSITE NUMBER is a
positive integer greater than 1
with more than two factors.
• 4, 6, 8, 9, and 10 are composite
numbers.
• The number 1 is neither PRIME or
COMPOSITE.
Tell whether each number is
Prime or Composite.
• 23?
• Prime: it only has two factors, 1
and 23.
• 129?
• Composite: it has more than
two factors: 1, 3, 43, and 129.
• 54?
• Composite: 1, 2, 27, 6, 9, etc.
Prime Factorization
• Writing a COMPOSITE
NUMBER as a PRODUCT of
its PRIME FACTORS shows
the PRIME FACTORIZATION
of the number.
• OR…
• Breaking a composite
number into prime factors
is Prime Factorization.
• Remember Factor Trees?
Factor Trees
• Use a factor tree to write
the prime factorization of
825.
825
5
165
33
5
• 825 = 5 • 5 • 3 • 11
• 825 = 52  3  11 with
Prime Factorization.
3
11
Greatest Common Factor (GCF)
•
•
•
•
•
•
You can use PRIME
FACTORIZATION to find the
Greatest Common Factor.
Any factors that are the same
for two or more numbers are
COMMON FACTORS.
A Common Factor for 12 and
10 is 2.
Common Factors for 12 and 24
are:
2, 3, 4, 6, and 12.
12 is the GREATEST COMMON
FACTOR.
Find the GCF for 40 and 60:
40
60
2
20
2
2
10
2
30
2
5
40 = 2  2  2  5
or
40 = 23  5
15
3
5
60 = 2  2  3  5
or
60 = 22  3  5
So, 2  2  5 = 22  5 = 20,
The GCF of 40 and 60 is 20.
Find the GCF for 6a3b and 4a2b
• Write the Prime
Factorization.
1. 6a3b = 2•3•a•a•a•b
2. 4a2b = 2•2•a•a • b
• What are the GCF?
1. GCF = 2 • a2 • b
2. The GCF of 6a3b and 4a2b =
2a2b
Example Problems:
• Use Prime Factorization to
find the GCF:
1. 12 and 87
12: 3 • 4
87: 3 • 29
2.
3 is the only Common Factor so it is the GCF
15m2n and 45m
15m2n: 3 • 5 • m • m • n
45m: 3 • 3 • 5 • m
3, 5, m are the common factors, so
15m is the GCF.
Section 4.4: Simplifying
Fractions
October 14th Notes
Continued
Finding Equivalent Fractions
• Hopefully this is Review!
• Find equivalent fractions
by multiplying or dividing
the numerator and
denominator by the same
nonzero factor.
• 4/12 = (Multiply)
• 4/12 = (Divide)
Example Problems:
• Find two fractions
equivalent to each
fraction.
1. 5/15 =
2. 10/12 =
3. 14/20 =
Fractions in Simplest Form
• A fraction is in simplest form
when the numerator and
the denominator have no
factors in common other
than 1.
• Use GCF to write a fraction
in simplest form.
Try these:
• 6/8
• 9/12
• 28/35
Word Problem…
• You survey your friends
about their favorite
sandwich and find that 8
out of 12, or 8/12, prefer
peanut butter. Write this
fraction in simplest form.
Simplest form of Variable
Fractions
• You can simplify fractions
that contain variables.
• Assume that no expression
has a denominator that
equals zero.
Write in Simplest Form.
• y/xy =
• 3ab2/12ab =
• 2mn/6m =
• 24x2y/8xy =
Assignment #23
• Pages 183: 23-43 odd.
• Pages 188: 19-35 odd and
36.