Calculators are being given more functionality with each upgrade. Prime factorisation has been around for quite a while, but can calculators find the HCF of two numbers for you?
Yes, but not directly.
Enter two numbers as a fraction and the calculator will simplify it. It's just divided by the HCF. In this case, 36 and 80 become 9 and 20, which are a quarter of the size, so the highest common factor of 36 and 80 is 4.
I wouldn't say this is particularly useful for (AQA) Higher tier students, as basic HCF questions don't come up in calculator papers. As for foundation, AQA 83003F 2022 asked for the HCF of 12 and 18, and AQA 83002F 2020 asked for the HCF of 75 and 105. For some students, this trick might save them a couple of marks.
I'm posting this idea mainly to be used as a discussion point in lessons, to get students thinking deeper about the Maths.
What about the LCM?
You can use the idea that \(LCM(a,b) = \frac{ab}{HCF(a,b)}\)
In this case \(\frac{36\times80}{4}=720\)
I don't see that as a shortcut and probably involves a deeper understanding of HCF and LCM than the listing method or comparing them in index form. Again, it's a discussion point to deepen understanding.
A final discussion...
Is it possible to use the calculator in a similar way to find the HCF of 3 numbers?
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