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I see that you've uploaded an image of a math exercise. Let me help by addressing the problems listed:

1. **Find the greatest number which exactly divides 54 and 72.**  
   This involves finding the Greatest Common Divisor (GCD) of 54 and 72.

2. **Find the greatest number which divides 45 and 55 leaving a remainder of 5 in each case.**  
   You need to subtract 5 from both numbers (i.e., 45-5=40 and 55-5=50) and then find the GCD of 40 and 50.

3. **Find the smallest number which when divided by 12 and 18 leaves a remainder of 9 in each case.**  
   First subtract the remainder from the divisors (i.e., 12-9=3 and 18-9=9), then find the Least Common Multiple (LCM) of these adjusted values.

4. **What is the maximum capacity of a measuring can that can be used to fill two containers having a capacity of 24 litres and 36 litres respectively?**  
   You need to find the GCD of 24 and 36, as the greatest common divisor represents the largest measure that will exactly divide both capacities.

Would you like me to solve these problems step-by-step? Let me know which one you'd prefer to focus on first, or if you want details on all of them.

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Here are some questions that extend the topics discussed:
1. What is the relationship between GCD and LCM in number theory?
2. How can the Euclidean algorithm help find the GCD of two numbers?
3. What other methods can be used to find the GCD or LCM besides prime factorization?
4. What is the importance of finding the GCD in real-life applications?
5. Can you explain how modular arithmetic relates to the problem of finding a remainder?

**Tip:** When finding a number that divides two others leaving a remainder, always start by subtracting the remainder from each number before finding the common divisor.

1. Find the greatest number which exactly divides 54 and 72.
2. Find the greatest number which divides 45 and 55 leaving a remainder of 5 in each case.
3. Find the smallest number which when divided by 12 and 18 leaves a remainder of 9 in each case.
4. What is the maximum capacity of a measuring can that can be used to fill two containers having a capacity of 24 litres and 36 litres respectively?

Solve math problems involving the greatest common divisor (GCD), least common multiple (LCM), and remainder conditions. This exercise includes finding the GCD of numbers like 54 and 72, and solving for divisors with specific remainder conditions.

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