# Factorising With Common Factors

The answer to this question is quite simple:

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Looking at the two photos, it is quite easy for a human to work out which person is in both pictures.

But imagine the Maths that would be needed, (coupled with some facial recognition software), for a computerised device to work this out.

Actually the program required is not too complicated. It could use a Database of Facial Images, a lookup table, and some mathematics in the form of Sort/Match array processing code.

But this is turning into a High School IT lesson, so let’s get back to the Maths!

In this lesson we will be looking at Algebra Terms in expressions, and working out if the separate terms have anything in common.

Once we have worked out the “Common Factor”, it is then a fairly simple task to rewrite our original expression in “Factor Form”, (eg. a Form which contains brackets).

Prime Factors and Factor Trees

Before we can do the Common Factor work for this lesson, we first need to review “Prime Factors”.

Image Copyright 2013 by Passy’s World of Mathematics

In the images shown here we are building “Factor Trees” to work out the Prime Factors.

The Tree shapes are actually upside down in these diagrams, and the ends of each branch are called the “leaves” and this is where our Prime Number factors end up.

We combine together the leaves on the ends of the branches, and this gives us our set of Prime Factors.

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Watch the videos in the following section if you do not already know how to make “Prime Factors” for numbers.

Prime Factors Videos

And finally watch this great music song video from “Math Rocks!”

Expanded Form and Factor Form

When we expanded brackets using the Distributive Rule, we created an answer containing no brackets which is called “Expanded Form”.

Expanded Form is useful when we wnat to solve an Equation, or draw a Graph on an X-Y Grid.

If you need to review expanding brackets, then check out our previous lesson at the link below:

http://passyworldofmathematics.com/expanding-brackets-using-distributive-rule/

In this lesson we are doing the reverse process of Expanding, which is called “Factorisation”.

Factorising results in us getting an Expression which contains brackets.

Factorised Expressions are used for locating the horizontal X-Axis cross-over points on Graphs.

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Factorising Steps

The steps we follow to convert an Expanded expression into a Factorised expression are as follows.

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Common Factor Examples

The following examples show how we do Factorisation to create answers that have a single bracket and are in Factor Form.

Image Copyright 2013 by Passy’s World of Mathematics

Image Copyright 2013 by Passy’s World of Mathematics

Image Copyright 2013 by Passy’s World of Mathematics

Common Factors Involving Exponents

When our initial terms contain variable letters and exponents, we need to expand out the exponents, and then see what letters we have in common.

The following examples show this; where numbers and letters are both broken down as low as they can go, and then the common factors identified.

Image Copyright 2013 by Passy’s World of Mathematics

Image Copyright 2013 by Passy’s World of Mathematics

Common Factors Involving a Negative Sign

In the example below, we have a negative sign on both items, which means the negative sign is a Common Factor.

We write the negative sign as a -1 when we include it in the expanded factors.

Image Copyright 2013 by Passy’s World of Mathematics

The following video shows how to find the Highest Common Factor (HCF), or Greatest Common Factor (GCF), using Factor Trees.

This next video shows how to do the greatest common factor a faster way than using Prime Factors.

Common Factor Games

“Fruit Shoot” is a fun game where you have to work out what the biggest Common Factor is, and then use the mouse to move onto the correct piece of fruit and click on it.

Click the following link to play this fun game:

http://www.sheppardsoftware.com/mathgames/fractions/GreatestCommonFactor.htm

In this next Game, we slide the bottom pink boxes to their correct position on the question grid.

Click the following link to play this fun game:

http://www.oswego.org/ocsd-web/match/dragflip.asp?filename=slanegcf

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