If (the product of the common positive factors of 36 and 48) = 999 +`9 xx`........., then the number which will come in the blank space is

Options

A. 81
B. 90
C. 9
D. 27

Answer

To solve the problem step by step, we need to find the product of the common positive factors of 36 and 48, and then determine the number that fits into the equation given.

### Step 1: Find the factors of 36 and 48
- **Factors of 36**: 1, 2, 3, 4, 6, 9, 12, 18, 36
- **Factors of 48**: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

### Step 2: Identify the common positive factors
The common factors of 36 and 48 are:
- 1, 2, 3, 4, 6, 12

### Step 3: Calculate the product of the common factors
Now, we need to calculate the product of these common factors:
- Product = 1 × 2 × 3 × 4 × 6 × 12

Calculating step by step:
1. \( 1 \times 2 = 2 \)
2. \( 2 \times 3 = 6 \)
3. \( 6 \times 4 = 24 \)
4. \( 24 \times 6 = 144 \)
5. \( 144 \times 12 = 1728 \)

So, the product of the common positive factors is **1728**.

### Step 4: Set up the equation
According to the problem, we have:
\[ 1728 = 999 + 9y \]

### Step 5: Solve for \( y \)
To find \( y \), we rearrange the equation:
\[ 9y = 1728 - 999 \]
\[ 9y = 729 \]

Now, divide both sides by 9:
\[ y = \frac{729}{9} = 81 \]

### Conclusion
The number that comes in the blank space is **81**.

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