Download 1.1 Prime Factorization - Greatest Common Factor. Math 8

1.1 Prime Factorization - Greatest Common Factor.
Math 8
Sort the following numbers in the table: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
Exactly one factor
Exactly two factors
2, 3, 5, 7
More than two factors
4, 6, 8, 9, 10
prime
composite
1
Neither prime nor composite
 A whole number with exactly two factors (1 and itself) is called a _ prime __.
 A whole number greater than 1 with more than two factors is called a __ composite _.
The numbers 0 and 1 are __neither__ prime _nor composite.
 A composite number may be written as the product of prime numbers.
This product is the _ prime factorization of the number.
Example 1 Find the prime factorization of 660.
660
Write the number as the product of two factors.
66
6
Continue to factor until only prime factors remain.
The prime factorization of 660 is
2
10
11
2
5
3
2 · 2 · 3 · 5 · 11 = 2² · 3 · 5 · 11
 The greatest of the factors common to TWO or more number is the greatest common factor (GCF).
Example 2 Find the greatest common factor of 36 and 60.
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
GCF = 6
Example 3 Find the greatest common factor of 90 and 120, using prime factorization.
90
9
3 3
120
10
2
12
5
6
2
10
2
5
90 =
2·3·3·5
=
120 =
2·2·2·3·5
=
GCF =
2 · 3·5
=
2 3
Example 4
Write
1. Divide by GCF.
30 = 2 · 15
45 = 3 · 15
=
in simplest form
2. Use prime factorization.
=
=
2 · 3² · 5
2³ · 3 · 5
30