Find the HCF of 24 and 34.

Options

A. 24
B. 2
C. 34
D. 17

Answer

To find the HCF (Highest Common Factor) of 24 and 34, we can follow these steps:

### Step 1: Find the Prime Factorization of Each Number
- **For 24**:
- Divide by 2: 24 ÷ 2 = 12
- Divide by 2: 12 ÷ 2 = 6
- Divide by 2: 6 ÷ 2 = 3
- Divide by 3: 3 ÷ 3 = 1
- So, the prime factorization of 24 is \( 2^3 \times 3^1 \).

- **For 34**:
- Divide by 2: 34 ÷ 2 = 17
- Divide by 17: 17 ÷ 17 = 1
- So, the prime factorization of 34 is \( 2^1 \times 17^1 \).

### Step 2: Identify the Common Prime Factors
- The prime factors of 24 are \( 2^3 \) and \( 3^1 \).
- The prime factors of 34 are \( 2^1 \) and \( 17^1 \).
- The only common prime factor is 2.

### Step 3: Determine the Lowest Power of the Common Prime Factor
- The lowest power of the common prime factor (which is 2) in both factorizations is \( 2^1 \).

### Step 4: Calculate the HCF
- Therefore, the HCF of 24 and 34 is \( 2^1 = 2 \).

### Final Answer
The HCF of 24 and 34 is **2**.

---