To find the quotient when dividing 592 by 16, we can follow these steps:
1. Set up the division: Write 592 as the dividend and 16 as the divisor.
[tex]\[
\begin{array}{r|l}
16 & 592 \\
\end{array}
\][/tex]
2. Determine how many times 16 goes into the first part of the dividend (592).
- Consider just the first two digits of the dividend, which is 59.
- 16 goes into 59 a certain number of times without exceeding it.
3. Estimate and check the multiplication:
- 16 goes into 59 about 3 times because \(16 \times 3 = 48\).
- Write 3 above the division bar.
[tex]\[
3
\begin{array}{r|r}
16 & 592 \\
\end{array}
\][/tex]
4. Subtract the result of the multiplication from the covered digits of the dividend:
- Subtract \(48\) ( \(16 \times 3\) ) from 59.
- \(59 - 48 = 11\).
So, you write the difference (11) below:
[tex]\[
\begin{array}{r|r}
16 & 592 \\
& - 48 \\
& \underline{11} \\
\end{array}
\][/tex]
5. Bring down the next digit (2 in this case) from the dividend to the right of 11, making it 112.
6. Determine how many times 16 goes into 112:
- 16 goes into 112 about 7 times because \(16 \times 7 = 112\).
- Write 7 above the division bar to the right of 3.
[tex]\[
37
\begin{array}{r|r}
16 & 592 \\
\end{array}
\][/tex]
7. Subtract again:
- Subtract \(112\) ( \(16 \times 7\) ) from 112.
- \(112 - 112 = 0\).
So, you write the difference (0) below:
[tex]\[
\begin{array}{r|r}
16 & 592 \\
& - 48 \\
& \underline{112} \\
& - 112 \\
& \underline{0} \\
\end{array}
\][/tex]
After these steps, we see that there is no remainder.
Therefore, the quotient when 592 is divided by 16 is [tex]\(37\)[/tex], and the remainder is [tex]\(0\)[/tex].
