Transcript Factoring - Brandywine School District

The Brandywine School District
Mathematics Department
presents
Factoring
For use with section 1.2
Discovering Mathematics Book 1A
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?
Let’s look at how many ways we
can arrange these six items
into a rectangular array.
2 rows of 3
or
3 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 number
are 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
2 4  8
4 2  8
The factors of the number
are 1, 2, 4, and 8
8
8 1  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
13
19and many many more!
Can you find a number with
more than four factors?
1 12  12
12 1  12 1 and 12 are factors of 12
2  6  12
6  2  12
12 has six factors:
2 and 6 are factors of 12
1, 2, 3, 4, 6, and 12.
3  4  12
4  3  12
3 and 4 are factors of 12
Numbers with exactly
two factors
are called
Prime Numbers
Which of these numbers are
PRIME NUMBERS?
11
13
19and many many more!
Why 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
2x3
You try it!
Write the Prime Factorization of
the following Composite Numbers:
9
10
21
22
3 3
25
3 7
2  11
You try it!
Write the Prime Factorization of
the following Composite Numbers:
8
12
16
2 4
2 6
2 Prime
23
Not
28
2 2 4
2 2 2 2
2 2 2
24
2  12
2 2 6
2 2 23