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.
- **For 12**:
- 12 can be divided by 2:
- \(12 \div 2 = 6\)
- \(6 \div 2 = 3\)
- \(3\) is a prime number.
- So, the prime factorization of 12 is \(2^2 \times 3^1\).

- **For 15**:
- 15 can be divided by 3:
- \(15 \div 3 = 5\)
- \(5\) is a prime number.
- So, the prime factorization of 15 is \(3^1 \times 5^1\).

- **For 27**:
- 27 can be divided by 3:
- \(27 \div 3 = 9\)
- \(9 \div 3 = 3\)
- \(3\) is a prime number.
- So, the prime factorization of 27 is \(3^3\).

### Step 2: Identify the common prime factors.
- The prime factorizations are:
- 12: \(2^2 \times 3^1\)
- 15: \(3^1 \times 5^1\)
- 27: \(3^3\)

- The only common prime factor among all three numbers is **3**.

### Step 3: Determine the lowest power of the common prime factor.
- The lowest power of the common prime factor (which is 3) in all three numbers is \(3^1\).

### Step 4: Conclude the HCF.
- Therefore, the HCF of 12, 15, and 27 is \(3\).

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

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