LCM & HCF

The following pencast shows you how to use the product of prime factors to find the HCF or LCM of two or more numbers.

This is very useful, especially for large numbers.
LCM - pick the highest power of each prime factor and multiply together.

HCF -  pick the lowest power of the common prime factors and multiply together.

HCF and LCM with Prime Factors
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Product of Prime Factors

If we take any number that is not a prime number we can write it as the product of 2 or more prime numbers. This means it can be made by multiplying prime numbers together. 

Click below to watch some examples using the "factor tree" method. Click the yellow arrow to make it bigger, you can jump backwards and forwards by clicking anywhere on the page.

Starter Notebook p. 13
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You can break these down in lots of different ways but the final answer will always be the same.

Remember: Product means "multiplied together".
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Factors in Algebra

It is important to know the four methods for finding factors that we use in algebra. These notes cover all four methods. they include guide number method for finding the factors of quadratic expressions, this method works for all quadratic expressions that have factors with whole numbers and does not require guessing or trial and error. Initially it may look complicated but that is because it includes explanations, once you get used to working this way it is quick and effective. It is a good idea to practice multiplying your factors together to check your answer and to help your understanding of factorising.

Tip: When factorising by grouping copy the first bracket and then work out what to put in front of it.

When factorising this

2cd – 2ca –3bd+ 3ab

factorise the first two terms

2c(d – a)

then repeat what is inside the bracket

2c(d – a)     (d– a)

then work out what should go in front of the bracket

2c(d – a) –3b(d– a)

finish by grouping the common factors

(2c–3b) (d –2a)

You are less likely to make mistakes with the signs when you do this.

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Factors - Third Year Revision

In third year the same types of factors are covered, but the questions might be a little harder.

Be able to recognise the four types of factors that you are likely to come across and  know how to factorise each type.

• Highest Common Factor - always check for a HCF first.
• Factorise by Grouping - you may need to regroup before you can factorise.
• Quadratic Expressions - the guide number method works well here especially if the coefficient of x squared is not one.
• The Difference of Two Squares.

Sometimes after you find the HCF you can break it down further - you might end up with 3 factors.

Notes and Examples here - also see second year post.

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