A milkman has two containers contain 75 liter and 45 liter milk respectively. What biggest measure that can measure the milk of both containers exactly ?

Options

A. 1 liter
B. 5 liter
C. 15 liter
D. 25 liter

Answer

To find the biggest measure that can measure the milk of both containers exactly, we need to calculate the Highest Common Factor (HCF) of the two quantities of milk: 75 liters and 45 liters.

### Step-by-Step Solution:

1. **Identify the quantities**:
- Container 1: 75 liters
- Container 2: 45 liters

2. **Find the prime factorization of each quantity**:
- For 75:
- Divide by 5: \( 75 \div 5 = 15 \)
- Divide by 5 again: \( 15 \div 5 = 3 \)
- So, the prime factorization of 75 is \( 5^2 \times 3^1 \) or \( 5 \times 5 \times 3 \).
- For 45:
- Divide by 5: \( 45 \div 5 = 9 \)
- Divide by 3: \( 9 \div 3 = 3 \)
- Divide by 3 again: \( 3 \div 3 = 1 \)
- So, the prime factorization of 45 is \( 5^1 \times 3^2 \) or \( 5 \times 3 \times 3 \).

3. **List the common prime factors**:
- The common prime factors of 75 and 45 are:
- \( 5 \) (minimum power is \( 1 \))
- \( 3 \) (minimum power is \( 1 \))

4. **Calculate the HCF**:
- HCF = \( 5^1 \times 3^1 = 5 \times 3 = 15 \)

5. **Conclusion**:
- The biggest measure that can measure the milk of both containers exactly is **15 liters**.