The HCF of 85 and 153 can be expressed in the form of 85m - 153. Calculate the value of m.

Options

A. 1
B. 5
C. `-1`
D. 2

Answer

To find the value of \( m \) in the equation \( 85m - 153 = \text{HCF}(85, 153) \), we will follow these steps:

### Step 1: Find the HCF of 85 and 153
To find the HCF, we can use the prime factorization method.

- **Prime factorization of 85**:
\[ 85 = 5 \times 17 \]

- **Prime factorization of 153**:
\[ 153 = 3 \times 51 = 3 \times 3 \times 17 = 3^2 \times 17 \]

### Step 2: Identify the common factors
From the prime factorizations:
- For 85: \( 5 \times 17 \)
- For 153: \( 3^2 \times 17 \)

The common factor is \( 17 \).

### Step 3: Set up the equation
Now that we have the HCF:
\[ \text{HCF}(85, 153) = 17 \]
We can substitute this into the equation:
\[ 85m - 153 = 17 \]

### Step 4: Solve for \( m \)
Rearranging the equation:
\[ 85m = 17 + 153 \]
\[ 85m = 170 \]

Now, divide both sides by 85:
\[ m = \frac{170}{85} \]
\[ m = 2 \]

### Final Answer
The value of \( m \) is \( 2 \).

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