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

Options

A. 7
B. 13
C. 62
D. 31

Explanation

To find the maximum capacity of a container that can measure the diesel from the three tankers (403 litres, 434 litres, and 465 litres) an exact number of times, we need to calculate the Highest Common Factor (HCF) of the three numbers. Here’s a step-by-step solution:

### Step 1: Find the prime factorization of each number.
1. **403**:
- Divide by 13: \( 403 ÷ 13 = 31 \)
- Therefore, the prime factorization of 403 is \( 13 \times 31 \).

2. **434**:
- Divide by 2: \( 434 ÷ 2 = 217 \)
- Now, factor 217: \( 217 ÷ 7 = 31 \)
- Therefore, the prime factorization of 434 is \( 2 \times 7 \times 31 \).

3. **465**:
- Divide by 3: \( 465 ÷ 3 = 155 \)
- Now, factor 155: \( 155 ÷ 5 = 31 \)
- Therefore, the prime factorization of 465 is \( 3 \times 5 \times 31 \).

### Step 2: Identify the common factors.
Now, we look for the common prime factors in all three numbers:
- From 403: \( 13, 31 \)
- From 434: \( 2, 7, 31 \)
- From 465: \( 3, 5, 31 \)

The only common factor among all three numbers is **31**.

### Step 3: Conclusion
The maximum capacity of a container that can measure the diesel from the three tankers an exact number of times is **31 litres**.

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