$72 \longdiv { 13,714 }$
To divide 13714 by 72, we are looking for the quotient and the remainder, which can be expressed in the form \(13714 = 72 \times q + r\), where \(q\) is the quotient and \(0 \leq r < 72\). We can perform this long division by looking at the dividend digits step by step.
We start by considering the first three digits of 13714, which is 137. Dividing 137 by 72, we find that \(72 \times 1 = 72\), and \(137 - 72 = 65\). Next, we bring down the next digit, which is 1, to make the number 651. Dividing 651 by 72, we find that \(72 \times 9 = 648\), and \(651 - 648 = 3\). Finally, we bring down the last digit, 4, to make the number 34. Dividing 34 by 72, we find that \(72 \times 0 = 0\), and \(34 - 0 = 34\). Therefore, the quotient is 190 and the remainder is 34.
We have found that \(13714 \div 72 = 190\) with a remainder of 34. This can be expressed as \(13714 = 190 \times 72 + 34\). Thus, the quotient is 190 and the remainder is 34, which can also be written as \(190 \frac{34}{72}\), and simplified as \(190 \frac{17}{36}\). The result of the division is \(\boxed{190 \text{ remainder } 34}\).
Imagine you are managing a large collection of items, such as 13714 books that need to be packed into boxes, where each box can hold exactly 72 books. To determine how many boxes will be completely filled, you perform the division 13714 ÷ 72. This calculation shows you that you can fill 190 boxes, and you will have 34 books remaining that will require an additional partial box. This method is fundamental in logistics, inventory management, and resource allocation.