This document provides information about finding the greatest common factor (GCF) of numbers and expressions. It explains that every number can be written as a product of prime numbers. To find the GCF, one identifies the common prime factors between two or more numbers or expressions. The document gives examples of finding the prime factorizations of numbers like 18 and 27. It also shows how to find the GCF of monomial expressions and gives the GCF of 12x3y2 and 8xy2 as 4xy2.

1. http://elcajondesastre.blogcindario.com/2006/12/index.html

2. Before we start looking for GCF’s, let’s see if there are
some clues that might help us along the way!
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Who knows, we might even come across some
“prime” suspects!

3. http://ts1.mm.bing.net/th?id=HN.607992770558756528&pid=15.1&P=0
Our “prime” suspects are really prime numbers!
Like the ones shown below.
Prime numbers have two distinct (different) factors
1 and themselves.
For example:
the factors of 2 are 1 and 2.
the factors of 3 are 1 and 3.
The number one is not a prime number.
Do you know why?

4. So what do prime numbers
have to do with finding a GCF?
Every number that is not
prime can be written as a
product of prime numbers.
So what does that mean?
Here’s an example:
18 = 2 x 9
9 = 3 x 3
So 18 = 2 x 3 x 3
2 and 3 are prime numbers!
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5. Let’s practice writing the prime factorization of some numbers.
Prime factorization just means to write a number
as a product of its prime factors.
There are some other clues we can use to help with this!
If a number is even, it is always divisible by 2.
Therefore the first prime factor of an even number is 2!
Let’s write 24 as a product of prime numbers.
24
2 12
2 6
2 3
So 24 = 2 x 2 x 2 x 3

6. What about 27? It is not a prime number, and it is not an even number.
What do we do?
Well, if we can’t divide by the first prime number, 2,
then we try the next prime number, 3.
If that doesn’t work, then we go to the next prime and so on,
until we find one that works.
This is why knowing your multiplication tables is so very important!
27 = 3 x 9
9 = 3 x 3
So 27 = 3 x 3 x 3
2
3
5
7
11
13
17
19

7. What about monomials?
Can they be written as a product of primes?
Sure they can!
Let’s take a look at 6𝑥2 𝑦3
6 = 2 ∙ 3
𝑥2 = 𝑥 ∙ 𝑥
𝑦3 = 𝑦 ∙ 𝑦 ∙ 𝑦
So 6𝑥2 𝑦3 = 2 ∙ 3 ∙ 𝑥 ∙ 𝑥 ∙ 𝑦 ∙ 𝑦 ∙ 𝑦
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8. 3𝑥2 ; 6𝑥3
3 ∙ 𝑥 ∙ 𝑥
2 ∙ 3 ∙ 𝑥 ∙ 𝑥 ∙ 𝑥
To find the GCF for monomials
– you need to find what they
have in common.
3𝑥2
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9. Let’s look at one more example.
Let’s find the GCF for 12𝑥3 𝑦2 and 8𝑥𝑦2
2 ∙ 2 ∙ 3 ∙ 𝑥 ∙ 𝑥 ∙ 𝑥 ∙ 𝑦 ∙ 𝑦
2 ∙ 2 ∙ 2 ∙ 𝑥 ∙ 𝑦 ∙ 𝑦
2 ∙ 2 ∙ 𝑥 ∙ 𝑦 ∙ 𝑦
4𝑥𝑦2
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10. Written by:
Genny Phillips
2/10/2015