To solve the division problem [tex]\( 8610 \div 42 \)[/tex], we will find the quotient and remainder through detailed long division steps.
1. Setup the Division:
Write 8610 (the dividend) under the long division symbol and 42 (the divisor) outside.
[tex]\[
\begin{array}{r|l}
42 & 8610 \\
\end{array}
\][/tex]
2. Determine the first digit of the Quotient:
- Compare 42 into the first digit of 8610 (which is 8). Since 8 is smaller than 42, we consider the first two digits (which are 86).
- Determine how many times 42 can go into 86. It goes in 2 times (since [tex]\(2 \times 42 = 84\)[/tex] and [tex]\(3 \times 42 = 126\)[/tex] which would be too much).
3. Subtract and Bring Down the Next Digit:
- Perform the subtraction: [tex]\(86 - 84 = 2\)[/tex].
- Bring down the next digit which is 1, making the new number to consider 21.
[tex]\[
\begin{array}{r|l}
42 & 8610 \\
& -84 \\
\hline
& 21
\end{array}
\][/tex]
4. Determine the next digit of the Quotient:
- Compare how many times 42 can go into 21. Since 21 is less than 42, it goes 0 times.
5. Bring Down the Next Digit:
- Bring down the next digit which is 0, making the new number 210.
[tex]\[
\begin{array}{r|l}
42 & 8610 \\
& -84 \\
\hline
& 210
\end{array}
\][/tex]
6. Determine the next digit of the Quotient:
- Determine how many times 42 can go into 210. It goes in 5 times (since [tex]\(5 \times 42 = 210\)[/tex]).
7. Subtract and Complete the Division:
- Perform the subtraction: [tex]\(210 - 210 = 0\)[/tex].
- There are no more digits left to bring down, and the remainder is 0.
[tex]\[
\begin{array}{r|l}
42 & 8610 \\
& -84 \\
\hline
& 210 \\
& -210 \\
\hline
& 0
\end{array}
\][/tex]
8. Final Quotient and Remainder:
- We have completed the division. The quotient is the number of times we have multiplied 42 to get 8610, which is 205.
- The remainder after the final step is 0.
Thus, when 8610 is divided by 42, the quotient is 205, and the remainder is 0.
