If (the sum of common positive factors of 15 and 90) = 15 `xx '-'` - 36, then the number which will come in blank is

Options

A. 15
B. 10
C. 5
D. 4

Answer

To solve the problem, we need to find the number that will fill in the blank in the equation:

\[ \text{(sum of common positive factors of 15 and 90)} = 15 \times \text{(blank)} - 36 \]

### Step 1: Find the factors of 15 and 90

**Factors of 15:**
- The factors of 15 are: 1, 3, 5, 15.

**Factors of 90:**
- The factors of 90 are: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90.

### Step 2: Identify the common factors

**Common factors of 15 and 90:**
- The common factors are: 1, 3, 5, 15.

### Step 3: Calculate the sum of the common factors

**Sum of common factors:**
- Sum = 1 + 3 + 5 + 15 = 24.

### Step 4: Set up the equation

Now we can substitute the sum of the common factors into the equation:

\[ 24 = 15 \times \text{(blank)} - 36 \]

### Step 5: Solve for the blank

**Rearranging the equation:**
- Add 36 to both sides:
\[ 24 + 36 = 15 \times \text{(blank)} \]
\[ 60 = 15 \times \text{(blank)} \]

**Dividing both sides by 15:**
\[ \text{(blank)} = \frac{60}{15} = 4. \]

### Conclusion

The number that will come in the blank is **4**.

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