The HCF of 12, 15 and 27 will be

Options

A. 2
B. 3
C. 4
D. 6

Answer

To find the HCF (Highest Common Factor) of the numbers 12, 15, and 27, we can follow these steps:

### Step 1: Find the Prime Factorization of Each Number
- **12**: The prime factorization of 12 is \(2 \times 2 \times 3\) or \(2^2 \times 3^1\).
- **15**: The prime factorization of 15 is \(3 \times 5\) or \(3^1 \times 5^1\).
- **27**: The prime factorization of 27 is \(3 \times 3 \times 3\) or \(3^3\).

### Step 2: List the Prime Factors
- The prime factors of 12 are \(2^2\) and \(3^1\).
- The prime factors of 15 are \(3^1\) and \(5^1\).
- The prime factors of 27 are \(3^3\).

### Step 3: Identify the Common Prime Factors
The only common prime factor among the three numbers is \(3\).

### Step 4: Determine the Lowest Power of the Common Prime Factor
- The lowest power of \(3\) that appears in all three factorizations is \(3^1\).

### Step 5: Conclusion
Thus, the HCF of 12, 15, and 27 is \(3\).

### Final Answer
The HCF of 12, 15, and 27 is **3**.

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