Find the greatest number that can divide 246 and 279 by leaving remainders 2 and 3, respectively.

Options

A. 4
B. 40
C. 6
D. 60

Answer

To find the greatest number that can divide 246 and 279 leaving remainders of 2 and 3 respectively, we can follow these steps:

### Step 1: Adjust the Numbers
First, we need to adjust the numbers 246 and 279 by subtracting the remainders from them.

- For 246, subtract the remainder 2:
\[ 246 - 2 = 244 \]
- For 279, subtract the remainder 3:
\[ 279 - 3 = 276 \]

### Step 2: Find the Greatest Common Divisor (GCD)
Next, we need to find the greatest common divisor (GCD) of the adjusted numbers 244 and 276.

#### Step 2.1: Prime Factorization
- **Prime factorization of 244**:
\[ 244 = 2 \times 122 = 2 \times 2 \times 61 = 2^2 \times 61 \]
- **Prime factorization of 276**:
\[ 276 = 2 \times 138 = 2 \times 2 \times 69 = 2^2 \times 3 \times 23 \]

#### Step 2.2: Identify Common Factors
Now, we identify the common factors from the prime factorizations:
- The common factor is \(2^2\).

### Step 3: Calculate the GCD
The GCD is:
\[ GCD = 2^2 = 4 \]

### Step 4: Conclusion
Thus, the greatest number that can divide 246 and 279 leaving remainders of 2 and 3 respectively is:
\[ \boxed{4} \]

---