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1. Lee is sewing vests using 16 green buttons and 24 blue buttons. All the vests are identical, and all have both green and blue buttons.

a. List the factors of 16 and 24. Then circle the common factors.

\begin{tabular}{|l|l|l|l|l|l|l|l|}
\hline
Factors of 16: & & & & & & & \\
& & \\
\hline
Factors of 24: & & & & & & & \\
\hline
\end{tabular}

b. What are the common factors of 16 and 24? \\
c. What are the possible numbers of vests Lee can make? \\
d. What is the greatest common factor (GCF) of 16 and 24? \\
e. What is the greatest number of vests Lee can make?



Answer :

GinnyAnswer
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]

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