If $96\div 3 = \fbox{$\phantom{0}$},$ then by the relationship between multiplication and division, we have

\[ \fbox{$\phantom{0}$}\times 3 = 96. \]

We start with the given multiplication problem:

\[ 30\times 3 = {\color{blue}{90}} \]

Let's now try the numbers in the list, starting with the smallest. We can use repeated addition to compute the products.

\begin{align*} 31\times 3 &= {\color{blue}{90}} + 3 = {\color{red}{93}} \qquad {\color{red}{\times}} \\[10pt] 32\times 3 &= {\color{red}{93}}\ + 3 =96 \qquad {\color{green}{\checkmark}} \end{align*}

Therefore, $96 \div 3 = 32.$

If $86 \div 2 = \fbox{$\phantom{0}$},$ then by the relationship between multiplication and division, we have \[ \fbox{$\phantom{0}$} \times 2 = 86. \]

We start with the given multiplication problem: \[ 40 \times 2 = {\color{blue}{80}} \]

Let's now try the numbers in the list, starting with the smallest. We can use repeated addition to compute the products. \begin{align*} 41 \times 2 & = {\color{blue}{80}} + 2 = {\color{red}{82}} \qquad{\color{red}{\times}} \\[10pt] 42 \times 2 & = {\color{red}{82}} + 2 = {\color{purple}{84}} \qquad{\color{red}{\times}} \\[10pt] 43 \times 2 & = {\color{purple}{84}} + 2 = 86 \qquad{\color{green}{\checkmark}} \end{align*}

Therefore, $86 \div 2 = 43.$

If $198\div 6 = \fbox{$\phantom{0}$},$ then by the relationship between multiplication and division, we have

\[ \fbox{$\phantom{0}$}\times 6 = 198. \]

We start with the given multiplication problem:

\[ 30\times 6 = {\color{blue}{180}} \]

Let's try the numbers in the list, starting with the smallest. We can use repeated addition to compute the products.

\begin{align*} 31\times 6 &= {\color{blue}{180}} + 6 = {\color{red}{186}}\qquad{\color{red}{\times}} \\[10pt] 32\times 6 &= {\color{red}{186}} + 6 ={\color{purple}{192}}\qquad{\color{red}{\times}} \\[10pt] 33\times 6 &= {\color{purple}{192}} + 6 =198 \quad{\color{green}{\checkmark}} \end{align*}

Therefore, $198 \div 6 = 33.$

If $615\div 5 = \fbox{$\phantom{0}$},$ then by the relationship between multiplication and division, we have

\[ \fbox{$\phantom{0}$}\times 5 = 615. \]

We start with the given multiplication problem:

\[ 120\times 5 = {\color{blue}{600}} \]

Let's try the numbers in the list, starting with the smallest. We can use repeated addition to compute the products.

\begin{align*} 121\times 5 &= {\color{blue}{600}} + 5 = {\color{red}{605}}\qquad{\color{red}{\times}} \\[10pt] 122\times 5 &= {\color{red}{605}} + 5 ={\color{purple}{610}}\qquad{\color{red}{\times}} \\[10pt] 123\times 5 &= {\color{purple}{610}} + 5 =615 \quad{\color{green}{\checkmark}} \end{align*}

Therefore, $615 \div 5 = 123.$

If $84\div 3 = \fbox{$\phantom{0}$},$ then by the relationship between multiplication and division, we have

\[ \fbox{$\phantom{0}$}\times 3 = 84. \]

We start with the given multiplication problem:

\[ 30\times 3 = {\color{blue}{90}} \]

Let's now try the numbers in the list, starting with the largest. We can use repeated subtraction to compute the products.

\begin{align*} 29\times 3 &= {\color{blue}{90}} - 3 = {\color{red}{87}}\qquad{\color{red}{\times}} \\[10pt] 28\times 3 &= {\color{red}{87}} - 3 =84 \qquad{\color{green}{\checkmark}} \end{align*}

Therefore, $84 \div 3 = 28.$

If $324 \div 9 = \fbox{$\phantom{0}$},$ then by the relationship between multiplication and division, we have \[ \fbox{$\phantom{0}$} \times 9 = 324. \]

We start with the given multiplication problem: \[ 40 \times 9 = {\color{blue}{360}} \]

Let's now try the numbers in the list, starting with the largest. We can use repeated subtraction to compute the products. \begin{align*} 39 \times 9 & = {\color{blue}{360}} - 9 = {\color{red}{351}}\qquad{\color{red}{\times}} \\[10pt] 38 \times 9 &= {\color{red}{351}} - 9 = {\color{purple} 342}\qquad{\color{red}{\times}} \\[10pt] 37 \times 9 &= {\color{purple}{342}} - 9 = {\color{magenta} 333}\qquad{\color{red}{\times}} \\[10pt] 36 \times 9 &= {\color{magenta}{333}} - 9 = 324 \qquad{\color{green}{\checkmark}} \end{align*}

Therefore, $324 \div 9 = 36.$