Three big drums contains 44 litres, 55 litres and 99 litres of diesel. What is the largest measure that can measure all the different quantities exactly?

Options

A. 9 litres
B. 120 litres
C. 11 litres
D. 70 litres

Answer

To find the largest measure that can measure all the different quantities of diesel in the drums exactly, we need to determine the highest common factor (HCF) of the three quantities: 44 liters, 55 liters, and 99 liters.

### Step-by-Step Solution:

**Step 1: Factor each quantity into its prime factors.**

- **For 44:**
- 44 can be factored as:
- 44 = 2 × 2 × 11
- Prime factorization: 2² × 11

- **For 55:**
- 55 can be factored as:
- 55 = 5 × 11
- Prime factorization: 5 × 11

- **For 99:**
- 99 can be factored as:
- 99 = 3 × 3 × 11
- Prime factorization: 3² × 11

**Step 2: Identify the common prime factors.**

Now we will look for the common prime factors in all three factorizations:
- 44: 2² × 11
- 55: 5 × 11
- 99: 3² × 11

The only common prime factor among all three numbers is **11**.

**Step 3: Determine the highest common factor (HCF).**

Since 11 is the only common factor, the highest common factor (HCF) of 44, 55, and 99 is:
- HCF = 11

### Conclusion:

The largest measure that can measure all the different quantities of diesel exactly is **11 liters**.

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