In this task, you are given the digits 1, 2, 3, 4, and 5, and you need to use these digits once to form two numbers for a division problem. The goal is to experiment with different combinations to achieve:

a) The smallest possible remainder
b) The greatest possible remainder
c) A remainder that is a multiple of 5

You are also encouraged to compare your results with a partner after experimenting with the combinations.

Here are some strategies to approach each part:

1. Smallest Possible Remainder (a):
   The smallest remainder occurs when the division results in a quotient that is as close to an integer as possible. You should aim for a division where the numbers are well-aligned in terms of divisibility.

2. Greatest Possible Remainder (b):
   To get the largest remainder, you need a division where the dividend is not too large compared to the divisor, which will leave a substantial part of the dividend unaccounted for in the quotient.

3. Remainder Multiple of 5 (c):
   Here, the remainder should be a multiple of 5, which could be 0 or 5. You need to experiment with divisors and dividends that will yield this remainder.

Let me know if you'd like to dive into specific calculations, or if you want suggestions for specific number combinations to achieve the given goals.

Would you like to explore detailed solutions for these divisions?
Here are 5 further questions related to this exercise:

1. How can the order of digits affect the remainder in a division problem?
2. What is the largest remainder you can obtain in any division using these digits?
3. Can you explain why some divisions leave no remainder at all?
4. How does the relationship between divisor and dividend influence the remainder?
5. Can you find a division where the remainder is exactly 5, and explain why?

Tip: For division problems, always check whether the dividend is evenly divisible by the divisor to get a remainder of 0.