Let's solve the given problem step-by-step.

Problem Breakdown:

The auditorium has rows of 8 seats. Kayla knows there are:

• At least 70 seats in total.
• Fewer than 150 seats in total.

We need to determine:

1. How to find the least possible number of rows.
2. How to find all possible numbers of rows without checking if 8 divides every number between 70 and 150.
3. Listing all the possible numbers of rows.

Solution:

1. Explain how to find the least possible number of rows.

To find the least number of rows:

• Each row has 8 seats. Therefore, the total number of seats is divisible by 8.
• Find the smallest multiple of 8 that is at least 70. This is done by dividing 70 by 8 and rounding up to the nearest whole number: $\text{Least rows} = \lceil 70 \div 8 \rceil = 9.$
• Multiply 9 rows by 8 seats: $9 \times 8 = 72 \text{ seats.}$ Thus, the least number of rows is 9.

2. How to find all possible numbers of rows without checking if 8 is a factor for every number between 70 and 150.

To find all possible rows:

• Start with the range of total seats: $70 \leq \text{Total Seats} < 150$.
• Total seats = $8 \times \text{rows}$. Rearrange this to: $\text{Rows} = \frac{\text{Total Seats}}{8}.$
• Total seats must be a multiple of 8. Find all multiples of 8 within $70 \leq \text{Total Seats} < 150$: $72, 80, 88, 96, 104, 112, 120, 128, 136, 144.$
• Divide these values by 8 to find the possible rows: $\text{Possible rows} = 9, 10, 11, 12, 13, 14, 15, 16, 17, 18.$

3. Name all the possible numbers of rows in the auditorium.

From the above calculation, the possible numbers of rows are: $\boxed{9, 10, 11, 12, 13, 14, 15, 16, 17, 18.}$

Final Answer:

1. The least possible number of rows is 9.
2. To find all possible rows, calculate multiples of 8 within $70$ to $150$ and divide by 8.
3. The possible numbers of rows are 9, 10, 11, 12, 13, 14, 15, 16, 17, 18.

Would you like further clarification or details?
Here are 5 related questions for further learning:

1. What is the greatest possible number of rows in this problem?
2. How can you generalize this method to any number of seats per row?
3. What if the total seats were between 100 and 200? How would this change the answer?
4. Why is finding multiples an efficient way to solve problems like this?
5. How does rounding up after division ensure accuracy in such problems?

Tip: For problems involving divisibility, focus on the multiples of the divisor within the range given—it simplifies the solution!