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Factoring
using GCF
interpret parts of an expressions
such as terms, factors, and
coefficient
What is a factor?
Lets recall the factors of 36:
Why are these factors of 36?
What is a factor?
You list the factors of 12:
What are the common factors
of 12 and 36?
Of these factors, which is the
greatest or the GCF?
For two or more nonzero whole numbers, a
common factor is a whole number that is a
factor of each number. The greatest common
factor (GCF) of two or more nonzero whole
numbers is the greatest of their common factors.
Example 1
Find the GCF of 30 and 42
Caution:
Do not confuse GCF with LCM.
A multiple of a whole number is the product of the number and
any nonzero whole number. A common multiple of two or more
whole numbers is a multiple of each number. The least common
multiple (LCM) of two or more whole numbers is the least of their
common multiples.
Example 2
Find
the LCM of 10 and 15
Also recall that, when factoring,...
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
Now lets apply GCF to
polynomials:
Example 3
Given
the polynomial
2x + 10, determine the
GCF.
Now lets apply GCF to
polynomials:
Given
the polynomial
6x-2y, determine the
GCF.
Now lets apply GCF to
polynomials:
Given
the polynomial
2x2 + 6x, determine
the GCF.
Now lets apply GCF to
polynomials:
Given
the polynomial
Find the GCF of 40a2b
and 48ab4, determine
the GCF.
Determine the GCF for each
of the following:
1.
2.
3.
4.
5.
Now let’s factor
Example 4
Factor
GCF
7x+14 using the
Factor
9x - 33 using
the GCF
Factor
x2 + 8x using
the GCF
Example 5
Factor :
Example
using GCF
6c d  12c d  3cd
3
2
2
Factor these on your
own looking for a GCF.
3
2
6. 6x  3x  12x
1.
2
2.
7. 5x  10x  35
3.
8. 16x y z  8x y z 12xy z
3 4
2 2 3
3 2