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 will follow these steps:

### Step 1: Factorize each number

1. **Factorizing 91**:
- 91 can be divided by 7:
\[ 91 \div 7 = 13 \]
- Therefore, the prime factorization of 91 is:
\[ 91 = 7 \times 13 \]

2. **Factorizing 112**:
- 112 is an even number, so we start dividing by 2:
\[ 112 \div 2 = 56 \]
\[ 56 \div 2 = 28 \]
\[ 28 \div 2 = 14 \]
\[ 14 \div 2 = 7 \]
- Since 7 is a prime number, we stop here. Therefore, the prime factorization of 112 is:
\[ 112 = 2^4 \times 7 \]

3. **Factorizing 49**:
- 49 can be divided by 7:
\[ 49 \div 7 = 7 \]
- Therefore, the prime factorization of 49 is:
\[ 49 = 7^2 \]

### Step 2: Identify the common factors

Now we have the prime factorizations:
- \( 91 = 7 \times 13 \)
- \( 112 = 2^4 \times 7 \)
- \( 49 = 7^2 \)

### Step 3: Find the common factors

The common factor among these numbers is 7.

### Step 4: Determine the HCF

Since 7 is the only common factor among all three numbers, the HCF of 91, 112, and 49 is:
\[ \text{HCF} = 7 \]

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

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