$70 \longdiv{61,261}$

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summerlampe33 summerlampe33

04-11-2026
Mathematics

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$70 \longdiv{61,261}$

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GinnyAnswer GinnyAnswer · Answer 1 · 2026-11-04T16:42:52-05:00

Set up the long division of $61,261$ by $70$.
Divide the initial digits to find the quotient digits: $612 \div 70 = 8$ remainder $52$; $526 \div 70 = 7$ remainder $36$; $361 \div 70 = 5$ remainder $11$.
State the result of the division: the quotient is $875$ and the remainder is $11$.
The final expression is $\boxed{875 \text{ remainder } 11}$.

Explanation

Problem Analysis and Setup

We are tasking with dividing the number $61,261$ by $70$. To do this, we can use the division algorithm, which states that any integer $a$ divided by a positive integer $b$ results in a quotient $q$ and a remainder $r$ such that $a = b \times q + r$, where $0 \leq r < b$. In this problem, $a = 61,261$ and $b = 70$.

Step-by-Step Long Division

We perform the long division by examining the digits of $61,261$:

Looking at the first three digits, $612$, we find how many times $70$ goes into it. Since $70 \times 8 = 560$ and $70 \times 9 = 630$, the quotient digit is $8$. Subtracting $560$ from $612$ leaves a remainder of $52$.
We bring down the next digit, $6$, making the current value $526$. We find how many times $70$ goes into $526$. Since $70 \times 7 = 490$ and $70 \times 8 = 560$, the quotient digit is $7$. Subtracting $490$ from $526$ leaves a remainder of $36$.
We bring down the final digit, $1$, making the current value $361$. We find how many times $70$ goes into $361$. Since $70 \times 5 = 350$, the quotient digit is $5$. Subtracting $350$ from $361$ leaves a final remainder of $11$.

Conclusion of Division and Final Answer The result of the division $61,261 \div 70$ is $875$ with a remainder of $11$. This can be written as $\boxed{875 \text{ remainder } 11}$.

Combining the results from our long division, we have a quotient of $875$ and a remainder of $11$. This means the division can be expressed as:
\[61,261 = 70 \times 875 + 11\]
Alternatively, this can be represented as a mixed number:
\[\frac{61,261}{70} = 875 + \frac{11}{70}\]
The decimal value is approximately $875.157142857$. However, in the context of long division, we express it as the quotient $875$ with a remainder of $11$.

Examples

Imagine you are organizing a large event with 61,261 guests, and you want to transport them to the venue using buses that can each hold 70 people. To find out how many full busloads you will have, you perform a division: $61,261 \div 70$. The quotient tells you that 875 buses will be completely full, and the remainder tells you that there will be 11 people left over who will require one additional bus to reach the destination! Understanding division with remainders is essential for logistics, resource allocation, and planning.