Q 59E - Intermediate Algebra

Question

The greatest common factor of $36$and $60$is $12$. Explain what this means.

Step-by-Step Solution

Answer

 This means the GCF of two non-zero integers, $36$ and $60$, is the greatest positive integer $12$ that divides both $36$ and $60$ without any remainder.

Step 1 Definition for GCF:

The greatest common factor (GCF) of two or more expressions is the largest expression that is a factor of all the expressions.

Step 2

$$\begin{gathered} 36=2\times 3\times 2\times 3 \\ 60=2\times 3\times 2\times 5 \end{gathered}$$

The GCF$$\begin{gathered} =2\times 3\times 2 \\ =12 \end{gathered}$$

So,The GCF of $36$ and $60$ is $12$ which means both $30$and $60$ gets divided by the greatest positive integer $12$ without any remainder.