Question

How can GCF be used in real life?

Answer 1

Hint: The greatest common factor, or GCF, is the greatest factor that divides two numbers. We use the greatest common factor many times in real life. We can simplify the given fraction to its simplest form or ratio by finding the greatest common factor of the numerator and the denominator.

Complete step by step answer:
We use GCF in many every-day life situations, let’s look at one example below,
Given below are the ingredients for a recipe for 10 cakes: 100g flour, 80g sugar, 50g butter, 2 eggs. We want to find the amount of ingredients we need to make 20 cakes. To find this, first, we need to find the ingredient required to make one cake. We can do this as follows,
To make 10 cakes, we need 100g flour, all cakes will need the same amount of flour. So, to make one cake we will need \[\dfrac{100}{10}\], here the numerator is 100, and the denominator is 10. The GCF of these two numbers is 10. Dividing numerator and denominator by the GCF, we get
\[\Rightarrow \dfrac{\dfrac{100}{10}}{\dfrac{10}{10}}=\dfrac{10}{1}=10g\]
We can find the required amount of other ingredients in the same way, as follows
Sugar for 1 cake: \[\dfrac{80}{10}=\dfrac{\dfrac{80}{10}}{\dfrac{10}{10}}=\dfrac{8}{1}=8g\].
Butter for 1 cake: \[\dfrac{50}{10}=\dfrac{\dfrac{50}{10}}{\dfrac{10}{10}}=\dfrac{5}{1}=5g\].
Egg for 1 cake: \[\dfrac{2}{10}=\dfrac{\dfrac{2}{2}}{\dfrac{10}{2}}=\dfrac{1}{5}=0.2\]
Now that we have ingredients for one cake, we can find the amount for 25 cakes by multiplying this by 25. Because all cakes will need the same amount. By doing this we get,
Flour for 25 cake: \[10\times 25=250g\]
Sugar for 25 cake: \[8\times 25=200g\]
Butter for 25 cake: \[5\times 25=125g\]
Eggs for 25 cake: \[0.2\times 25=5\]

Note:
There are many other real-life situations, where we can use the GCF. The GCF makes calculation very easy. Without GCF we will have to deal with fractions with very large numerators, and denominators, which can become very inconvenient for doing calculations.