Find the HCF of 91, 112 and 49.

Options

A. 7
B. 9
C. 49
D. 11

Answer

To find the HCF (Highest Common Factor) of the numbers 91, 112, and 49, we can follow these steps:

### Step 1: Find the prime factorization of each number.
- **For 91**:
- 91 can be divided by 7 (since 91 ÷ 7 = 13).
- So, the prime factorization of 91 is \(7 \times 13\).

- **For 112**:
- 112 can be divided by 2 (since 112 is even).
- 112 ÷ 2 = 56
- 56 ÷ 2 = 28
- 28 ÷ 2 = 14
- 14 ÷ 2 = 7
- So, the prime factorization of 112 is \(2^4 \times 7\).

- **For 49**:
- 49 can be divided by 7 (since 49 ÷ 7 = 7).
- So, the prime factorization of 49 is \(7^2\).

### Step 2: List the prime factors.
- The prime factors of 91 are \(7, 13\).
- The prime factors of 112 are \(2, 7\).
- The prime factors of 49 are \(7\).

### Step 3: Identify the common factors.
- The only common prime factor among 91, 112, and 49 is \(7\).

### Step 4: Determine the HCF.
- Since \(7\) is the only common factor, the HCF of 91, 112, and 49 is \(7\).

### Final Answer:
The HCF of 91, 112, and 49 is **7**.

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