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# Factors and Multiples – and a clever disguise

For today’s post I am going to look at the  exam question on factors here.

You can see from the question that we are in the area of common factors and multiples, but the question does come with a bit of a disguise!

Look at that last line – We have been asked to find the highest value of a/b.   So how does a fraction have the highest value?

By making the top as high as possible, and the bottom as low as possible.

So a is the HIGHEST common factor of 72 and 96
and b is the LOWEST common Multiple of 6 and 9.

Its a question about our old friends LCM and HCM – we have see through the disguise!

Let’s find the answer now though. We start by giving our four naumbers in Prime Factor form.

9 = 3 x 3  = 32
6 = 2 x 3

72 = 2 x 2 x 2 x 3 x 3  = 23 x 32
120 = 2 x 2 x 2 x 3 x 5 = 23 x 3 x 5

For the LCM we take the largest power of each prime number included

LCM = 2 x 32 = 18 (=b)

For the HCF we take the largest power of each prime number included

HCF = 23 x 3 = 24 (=a)

So a/b  = 24/18 = 4/3 or 1 1/3