factoring for use with section 1.2 discovering mathematics book 1a the brandywine school district...
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FactoringFor use with section 1.2
Discovering Mathematics Book 1A
The Brandywine School District Mathematics Department
presents
What do we mean when we ask you to find the factors of a number?
Example: Find the factors of the number
Let’s look at how many ways we can arrange these six items into a rectangular array.
1 row of 6 or
6 rows of 1
1 and 6 are both factors
of the number 6
Can we make any other rectangular
arrays with six objects?
2 rows of 3
Let’s look at how many ways we can arrange these six items into a rectangular array.
or3 rows of 2
2 and 3 are both factors
of the number 6
Can we make any other rectangular
arrays with six objects?
The factors of the numberare 1, 2, 3, and 6
1 6 6 6 1 6 2 3 6 3 2 6
You try it! Find the factors of the number
1 8 8
8 1 8
2 4 8 4 2 8
The factors of the
number 8are 1, 2, 4, and 8
Do all whole numbers have exactly four factors?Can you find a number with fewer than four factors?Can you find a number with more than four factors?
Can you find a number with fewer than four factors?
11
7
53
2
113
17
19
and many many more!
Can you find a number with more than four factors? 1
21 12 12 12 1 12 1 and 12 are factors of
122 6 12 6 2 12 2 and 6 are factors of
123 4 12 4 3 12 3 and 4 are factors of
12
12 has six factors: 1, 2, 3, 4, 6, and 12.
Numbers with exactly two factors
are called
Prime Numbers
11
7
53
2
113
17
19
and many many more!
Which of these numbers are
PRIME NUMBERS?
1Why isn’t
PRIME?
1 1 1
The number 1 has only one factor!
Prime numbers have exactly two factors.
Whole numbers greater than one that aren’t prime numbers are called
Composite Numbers.
Writing whole numbers as the products of prime numbers!
Recall: The factors of the number 6 are 1, 2, 3, and 6
Only two of those factors are prime numbers.
The prime factorization of six is 2 x 3
You try it! Write the Prime Factorization of the following Composite Numbers:9 1
021
223 3 2 5 3 7 2 11
You try it! Write the Prime Factorization of the following Composite Numbers:8 1
216
242 4
Not Prime
2 2 2
2 62 2 3
2 82 2 4
2 2 2 2
2 122 2 6 2 2 2 3