Answer :
Let's solve the problem in a detailed, step-by-step manner:
### Step 1: List the Factors of 16 and 24
#### Factors of 16:
To find the factors of 16, we need to find all numbers that can divide 16 without leaving a remainder. The factors of 16 are:
[tex]\[ 1, 2, 4, 8, 16 \][/tex]
#### Factors of 24:
Similarly, to find the factors of 24, we need to find all numbers that can divide 24 without leaving a remainder. The factors of 24 are:
[tex]\[ 1, 2, 3, 4, 6, 8, 12, 24 \][/tex]
We can list these factors in a table:
[tex]\[ \begin{tabular}{|l|l|l|l|l|l|l|l|} \hline Factors of 16: & 1 & 2 & 4 & 8 & 16 & & \\ \hline Factors of 24: & 1 & 2 & 3 & 4 & 6 & 8 & 12 & 24 \\ \hline \end{tabular} \][/tex]
### Step 2: Circle the Common Factors
Now, let's identify and circle the common factors of 16 and 24. These are the factors that are found in both lists:
[tex]\[ 1, 2, 4, 8 \][/tex]
### Step 3: Identify the Common Factors, Possible Numbers of Vests, and the GCF
#### Common Factors of 16 and 24:
The common factors are:
[tex]\[ 1, 2, 4, 8 \][/tex]
#### Possible Numbers of Vests Lee Can Make:
Since all the vests must have both green and blue buttons, the number of vests Lee can make corresponds to the common factors. Therefore, the possible numbers of vests are:
[tex]\[ 1, 2, 4, 8 \][/tex]
#### Greatest Common Factor (GCF) of 16 and 24:
The greatest common factor (GCF) is the largest of the common factors. Hence, the GCF is:
[tex]\[ 8 \][/tex]
### Step 4: State the Greatest Number of Vests Lee Can Make
The greatest number of vests Lee can make, given the constraints, is:
[tex]\[ 8 \][/tex]
### Conclusion:
\begin{tabular}{|l|l|l|l|l|l|l|l|}
\hline
Factors of 16: & 1 & 2 & 4 & 8 & 16 & & \\
\hline
Factors of 24: & 1 & 2 & 3 & 4 & 6 & 8 & 12 & 24 \\
\hline
\end{tabular}
- What are the common factors of 16 and 24? [tex]\( 1, 2, 4, 8 \)[/tex]
- What are the possible numbers of vests Lee can make? [tex]\( 1, 2, 4, 8 \)[/tex]
- What is the GCF of 16 and 24? [tex]\( 8 \)[/tex]
- What is the greatest number of vests Lee can make? [tex]\( 8 \)[/tex]
### Step 1: List the Factors of 16 and 24
#### Factors of 16:
To find the factors of 16, we need to find all numbers that can divide 16 without leaving a remainder. The factors of 16 are:
[tex]\[ 1, 2, 4, 8, 16 \][/tex]
#### Factors of 24:
Similarly, to find the factors of 24, we need to find all numbers that can divide 24 without leaving a remainder. The factors of 24 are:
[tex]\[ 1, 2, 3, 4, 6, 8, 12, 24 \][/tex]
We can list these factors in a table:
[tex]\[ \begin{tabular}{|l|l|l|l|l|l|l|l|} \hline Factors of 16: & 1 & 2 & 4 & 8 & 16 & & \\ \hline Factors of 24: & 1 & 2 & 3 & 4 & 6 & 8 & 12 & 24 \\ \hline \end{tabular} \][/tex]
### Step 2: Circle the Common Factors
Now, let's identify and circle the common factors of 16 and 24. These are the factors that are found in both lists:
[tex]\[ 1, 2, 4, 8 \][/tex]
### Step 3: Identify the Common Factors, Possible Numbers of Vests, and the GCF
#### Common Factors of 16 and 24:
The common factors are:
[tex]\[ 1, 2, 4, 8 \][/tex]
#### Possible Numbers of Vests Lee Can Make:
Since all the vests must have both green and blue buttons, the number of vests Lee can make corresponds to the common factors. Therefore, the possible numbers of vests are:
[tex]\[ 1, 2, 4, 8 \][/tex]
#### Greatest Common Factor (GCF) of 16 and 24:
The greatest common factor (GCF) is the largest of the common factors. Hence, the GCF is:
[tex]\[ 8 \][/tex]
### Step 4: State the Greatest Number of Vests Lee Can Make
The greatest number of vests Lee can make, given the constraints, is:
[tex]\[ 8 \][/tex]
### Conclusion:
\begin{tabular}{|l|l|l|l|l|l|l|l|}
\hline
Factors of 16: & 1 & 2 & 4 & 8 & 16 & & \\
\hline
Factors of 24: & 1 & 2 & 3 & 4 & 6 & 8 & 12 & 24 \\
\hline
\end{tabular}
- What are the common factors of 16 and 24? [tex]\( 1, 2, 4, 8 \)[/tex]
- What are the possible numbers of vests Lee can make? [tex]\( 1, 2, 4, 8 \)[/tex]
- What is the GCF of 16 and 24? [tex]\( 8 \)[/tex]
- What is the greatest number of vests Lee can make? [tex]\( 8 \)[/tex]
