Question

What is the greatest common factor of 9 and 72?

Answer 1

The Greatest Common Factor of 9 and 72 is: 9

SOLUTION

Problem Statement

The question asks us to find the greatest common factor of 9 and 72.

Method

In order to solve this question, we just need to follow these steps:

1. Write out the prime factors of 9 and 72

2. Choose the common factors from both expressions.

3. Multiply the common factors.

Implementation

1. Write out the prime factors of 9 and 72:

`\begin{gathered} 9=1*3*3 \\ \text{The common factors of 9 are: 3 and 3} \\ \\ 72=1*2*2*2*3*3 \\ \text{Common factors of 72 are: 1,2, 2, 2 and 3, 3} \end{gathered}`

2. Choose the common factors from both expressions.:

We need to examine the two expressions for 9 and 72 above. Choose the common values.

`\begin{gathered} 3*3\text{ is common to both 9 and 72} \\ i\mathrm{}e\text{.} \\ 9\text{ is common to both 9 and 72} \\ 3\text{ is common to both 9 and 72 as well} \\ 1\text{ is also common to both 9 and 72} \end{gathered}`

3. Multiply the common factors.:

`\begin{gathered} \text{Thus, choosing the greatest values from 1,3 and 9.} \\ \therefore\text{The Greatest Common Factor = 9} \end{gathered}`

Final Answer:

The Greatest Common Factor of 9 and 72 is: 9