Xander Torres

2023-02-25

How can GCF be used in real life?

Talon Mcfarland

We use greatest common factors all the time with fractions, and as fractions are used a lot in everyday life, this makes GCF very useful!
By finding the GCF of the denominator and numerator, you can then successfully simplify a fraction or ratio.
E.g. We can simplify $\frac{30}{45}$ by knowing that its HCF is $15$.
Then we divide both parts by the HCF to simplify.
$\frac{\frac{30}{15}}{\frac{45}{15}}=\frac{2}{3}$
It also works for ratios, where you can simplify each side using HCF to find out a $1:X$ ratio. This can be useful if you are using a ratio for a recipe or order as you can use one piece of information to find out the right ratio for any combination.
So, to put this into a situation, say you know that for every 5 people at a party, you need 15 sandwiches. The HCF of these two numbers is 5, so for each person you need:
$\left(\frac{5}{5}\right):\left(\frac{15}{5}\right)=1:3$
3 sandwiches.
Now, if 16 people come to your party, you know you have to make $16×3=48$ sandwiches.
A final example is with recipes.
Math can be very helpful in this situation!
Here is a recipe for 10 cupcakes along with the serving size ratios for each:
100g flour = 10 people:100g = 1:10
80g sugar = 10 people:80g = 1:8
50g butter = 10 people:50g = 1:5
2 eggs = 10 people:2 eggs = 1:0.2 eggs
So, if we want to give cakes to all our friends, and need 25 cupcakes (what a popular mathematician!) then you can just multiply out this ratio.
Flour = 1:10 = 25:250
80g sugar = 1:8 = 1:200
50g butter = 1:5 = 25:125
2 eggs = 1:0.2 eggs = 25:5

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