Question

How do you find the greatest common factor of 24 and 22?

Answer 1

See explanation.

Explanation:

You cando it in at least two ways:

`1.` Do prime decomposition of the two numbers and find the longest group of repeating prime numbers:

`24=color(blue)(2)*2*2*3`

`22=color(blue)(2)*11`

The only rrepeating number is `2` (which I marked in blue), so it is the GCF of those numbers.

`2.` You can use Euclidean algorythm which is to subtract the smaller number from the larger one as long as the numbers are not the same, when they are they are also equal to the GCF of the start numbers.

Here you would get:

`gcd(24,22)=gcd(2,22)=gcd(2,20)=gcd(2,18)=gcd(2,2)=2`

You can find more about the algorithm on Wikipedia