Transcript Prime Factorization GCF notes

Objectives
The student will be able to:
1. find the prime factorization of a number.
2. find the greatest common factor (GCF) for
a set of monomials.
A prime number is a
number that can only be divided by
only one and itself.
A composite number is a number
greater than one that is not prime.
Prime or composite?
37
prime
51
composite
Prime or Composite?
89
1.
2.
3.
4.
Prime
Composite
Both
Neither
1) Find the prime factorization of 84.
84 = 4 • 21
= 2•2•3•7
= 22 • 3 • 7
2) Find the prime factorization of -210.
-210
= -1 • 210
= -1 • 30 • 7
= -1 • 6 • 5 • 7
= -1 • 2 • 3 • 5 • 7
3) Find the prime factorization of
45a2b3
45a2b3 =
9•5•a•a•b•b•b
= 3•3•5•a•a•b•b•b
= 32 • 5 • a • a • b • b • b
Write the variables without exponents.
What is the prime factorization of 48?
1.
2.
3.
4.
3  16
344
2234
22223
The Greatest Common Factor
(GCF) of 2 or more numbers is
the largest number that can divide
into all of the numbers.
4) Find the GCF of 42 and 60.
Write the prime factorization of
each number.
Greatest Common Factor (GCF)
The GCF is extremely important
when simplifying or reducing
fractions.
4) Find the GCF of 42 and 60.
42 =
60 =
2 • 3 • 7
2•2•3•5
What prime factors do the numbers
have in common?
Multiply those numbers.
The GCF is 2 • 3 = 6
6 is the largest number that can go
into 42 and 60!
5) Find the GCF of 40a2b and 48ab4.
40a2b = 2 • 2 • 2 • 5 •
a•a•b
48ab4 = 2 • 2 • 2 • 2 • 3 • a • b • b • b • b
What do they have in common?
Multiply the factors together.
GCF = 8ab
What is the GCF of 48 and 64?
1.
2.
3.
4.
2
4
8
16