# What is the GCF for 54, 72?

Jun 22, 2016

Greatest Common Factor is $18$

#### Explanation:

Factors of $54$ are $\left\{1 , 2 , 3 , 6 , 9 , 18 , 27 , 54\right\}$

Factors of $72$ are $\left\{1 , 2 , 3 , 4 , 6 , 8 , 9 , 12 , 18 , 24 , 36 , 72\right\}$

Hence common factors are $\left\{1 , 2 , 3 , 6 , 9 , 18\right\}$

and Greatest Common Factor is $18$

Jul 1, 2016

The GCF of $72$ and $54$ is $18$.

#### Explanation:

One way of finding the GCF of two numbers goes as follows:

• Divide the larger number by the smaller to give a quotient and remainder.

• If the remainder is $0$ then the smaller number is the GCF.

• Otherwise repeat with the smaller number and the remainder.

In our example, we find:

$\frac{72}{54} = 1$ with remainder $18$

$\frac{54}{18} = 3$ with remainder $0$

So the GCF is $18$.

Aug 8, 2016

18

#### Explanation:

Find the prime factors of each number and see how many factors are shared by both numbers.

$\text{ } 54 = 2 \times \textcolor{w h i t e}{2 \times 2} \times 3 \times 3 \times 3$
$\text{ } 72 = 2 \times 2 \times 2 \times 3 \times 3$
GCF=$\text{ " 2color(white)(2xx2xx)xx3xx3" } = 18$