Three tankers contain 403 litres, 434 litres, 465 litres of diesel respectively. Then the maximum capacity of a container that can measure the diesel of the three containers exact number of times is

Options

A. 31 litres
B. 62 litres
C. 41 litres
D. 84 litres

Answer

To find the maximum capacity of a container that can measure the diesel from three tankers (403 liters, 434 liters, and 465 liters) an exact number of times, we need to determine the highest common factor (HCF) of these three numbers.

### Step-by-step Solution:

1. **Identify the numbers**: We have three tankers with the following capacities:
- Tanker 1: 403 liters
- Tanker 2: 434 liters
- Tanker 3: 465 liters

2. **Find the prime factorization of each number**:
- For **403**:
- 403 = 13 × 31
- For **434**:
- 434 = 14 × 31 = 2 × 7 × 31
- For **465**:
- 465 = 15 × 31 = 3 × 5 × 31

3. **Identify the common factors**:
- The common prime factor in all three numbers is **31**.

4. **Determine the HCF**:
- Since 31 is the only common factor among the three numbers, the HCF of 403, 434, and 465 is **31**.

5. **Conclusion**:
- The maximum capacity of a container that can measure the diesel from all three tankers an exact number of times is **31 liters**.