To solve the division problem [tex]\( 6422 \div 2 \)[/tex], we will follow these steps:
1. Setting up the division:
[tex]\[
\require{enclose}
2 \enclose{longdiv}{6422}
\][/tex]
2. Divide the first digit:
- How many times does 2 go into 6? It goes 3 times as [tex]\( 2 \times 3 = 6 \)[/tex].
- Place the 3 above the line.
- Subtract [tex]\( 6 - 6 = 0 \)[/tex].
[tex]\[
\require{enclose}
\begin{array}{r|l}
& 3 \\[-3pt]
2 & \enclose{longdiv}{6420} \\
& 6 \\
\end{array}
\][/tex]
3. Bring down the next digit (which is 4). Now we have:
- How many times does 2 go into 4? It goes 2 times as [tex]\( 2 \times 2 = 4 \)[/tex].
- Place the 2 above the line.
- Subtract [tex]\( 4 - 4 = 0 \)[/tex].
[tex]\[
\require{enclose}
\begin{array}{r|l}
& 32 \\
2 & \enclose{longdiv}{6420} \\
& 6 \\[-3pt]
& 4 \\
& 4 \\
\end{array}
\][/tex]
4. Bring down the next digit (which is 2). Now we have:
- How many times does 2 go into 2? It goes 1 time as [tex]\( 2 \times 1 = 2 \)[/tex].
- Place the 1 above the line.
- Subtract [tex]\( 2 - 2 = 0 \)[/tex].
[tex]\[
\require{enclose}
\begin{array}{r|l}
& 321 \\
2 & \enclose{longdiv}{6420} \\
& 6 \\[-3pt]
& 4 \\
& 4 \\[-3pt]
& 2 \\
& 2 \\
\end{array}
\][/tex]
5. Bring down the final digit (which is 2). Now we have:
- How many times does 2 go into 2? It goes 1 time as [tex]\( 2 \times 1 = 2 \)[/tex].
- Place the 1 above the line.
- Subtract [tex]\( 2 - 2 = 0 \)[/tex].
[tex]\[
\require{enclose}
\begin{array}{r|l}
& 3211 \\
2 & \enclose{longdiv}{64220} \\
& 6 \\[-3pt]
& 4 \\
& 4 \\[-3pt]
& 2 \\
& 2 \\[-3pt]
& 2 \\
\end{array}
\][/tex]
In conclusion, after performing the division, we find that:
[tex]\[ \frac{6422}{2} = 3211 \][/tex]
The quotient is [tex]\( 3211 \)[/tex] and the remainder is [tex]\( 0 \)[/tex].
So, the answer to the division problem [tex]\( 6422 \div 2 \)[/tex] is:
[tex]\[ \boxed{3211} \][/tex] with a remainder of [tex]\( \boxed{0} \)[/tex].
