Transcript lesson 4-3

Factor
A factor of an integer is any
integer that divides the
given integer with no
remainder.
Prime Number
A prime number is a natural
number greater than one
that has exactly two positive
factors: one and itself.
Exercise
Write the prime factorization
of the number.
12
22 x 3
Exercise
Write the prime factorization
of the number.
18
2 x 32
Exercise
Write the prime factorization
of the number.
15
3x5
Exercise
List in order all the factors
of 12.
1, 2, 3, 4, 6, 12
Exercise
List in order all the factors
of 18.
1, 2, 3, 6, 9, 18
Exercise
List in order all the factors
of 15.
1, 3, 5, 15
Greatest Common Factor
The greatest common factor
(also known as the greatest
common divisor) is the
largest number that is a factor
of all the given numbers.
What is the GCF of
12 and 18?
Factoring to Find the Greatest
Common Factor
1. Write the prime factorization
of each number.
2. Identify the prime factors
common to all the given
numbers.
3. Find the product of the
common prime factors.
Example 1
Find the GCF of 24 and 36.
24 = 2 • 2 • 2 • 3
36 = 2 • 2 • 3 • 3
GCF = 2 • 2 • 3 = 12
Example 2
Find the GCF of 180 and 600.
180 = 2 • 2 • 3 • 3 • 5
600 = 2 • 2 • 2 • 3 • 5 • 5
GCF = 2 • 2 • 3 • 5 = 60
Relatively Prime
Numbers are relatively prime
if their greatest common
factor is one.
Example 3
Find the GCF of the three
numbers 1,764; 630; and 252.
1,764 = 2 • 2 • 3 • 3 • 7 • 7
630 = 2 • 3 • 3 • 5 • 7
252 = 2 • 2 • 3 • 3 • 7
GCF = 2 • 3 • 3 • 7 = 126
4x
2
4x
2
3ab
2
5a b
3y
4z
Example 4
Find the GCF of 15x3y and
21x2.
15x3y = 3 • 5 • x • x • x • y
21x2 = 3 • 7 • x • x
GCF = 3 • x • x = 3x2
Exercise
Find the GCF of the numbers
given in factored form.
23 • 32 and 22 • 32
36
Exercise
Find the GCF of the numbers
given in factored form.
2 • 32 • 11 and 3 • 5 • 112 33
Exercise
Find the GCF of the numbers
given in factored form.
22 • 3 • 52 and 22 • 52 • 7 100
Exercise
Find the GCF of the numbers
given in factored form.
3 • 5, 22 • 5 and 23 • 3 1
Exercise
Find the GCF of the numbers
given in factored form.
2 • 32, 2 • 3 • 5 and 22 • 3 • 5 6
Exercise
Find the GCF of the numbers
given in factored form.
23 • 52 • 11, 22 • 5 • 72 20
and 24 • 53 • 7