# How do you find the greatest common factor of 20, 16?

Oct 30, 2016

#### Answer:

The greatest common factor of $20$ and $16$ is: $4$.

#### Explanation:

The greatest common factor of a set of numbers is the largest of the numbers that divide exactly all the numbers in the set. For example, if we calculate the GCF of 20 and 16, we first find the factors of both numbers. Of these, there will be some factors that are both (at least always be a common factor: the number 1). Well, these common factors, the higher is the GCF.

16 factors are: 1, 2, 4, 8 and 16.

20 factors are 1, 2, 4, 5, 10 and 20.

Numbers that are factors of 16 and 20: 1, 2, 4.

The greatest of these is 4.

There are a more useful method to calculate GCF of a set of numbers:

1. Factorize all numbers in the set
2. Take a factor of each base that is repeated with exponent equals to the lowest of they.
3. Multiply the factors taken. The result is GCF.

Come on to see an example:

We want calculate $G C F \left\{20 , 32 , 48\right\}$

First, we factorize the numbers:

$20 = {2}^{2} \cdot 5$
$32 = {2}^{5}$
$48 = {2}^{4} \cdot 3$

Now, we take a factor from bases repeated, i.e. we take only a $2$, because the other bases ($3$ and $5$) are no common to the three numbers. The $2$ with the lowest exponent is ${2}^{2}$.

The GCF is:

$G C F \left\{20 , 32 , 48\right\} = {2}^{2} = 4$.