6480, 1080, 216, 54, ? , 9

Options

A. 12
B. 17
C. 19
D. 18

Explanation

To find the missing number in the series: 6480, 1080, 216, 54, ?, 9, we can observe the pattern in the series. Let's break it down step by step.

### Step 1: Identify the pattern
We can see that each number in the series is obtained by dividing the previous number by a certain value.

### Step 2: Calculate the first division
- Start with the first two numbers:
\[ 6480 \div 6 = 1080 \]
This shows that we divide 6480 by 6 to get 1080.

### Step 3: Calculate the second division
- Now, take the next pair:
\[ 1080 \div 5 = 216 \]
This indicates that we divide 1080 by 5 to get 216.

### Step 4: Calculate the third division
- Next, we look at:
\[ 216 \div 4 = 54 \]
This means we divide 216 by 4 to get 54.

### Step 5: Calculate the fourth division
- Now, we need to find the missing number (let's call it \( x \)):
\[ 54 \div 3 = x \]
Calculating this gives:
\[ x = 54 \div 3 = 18 \]

### Step 6: Verify with the next number
- Finally, we check if this fits with the next number in the series:
\[ 18 \div 2 = 9 \]
This confirms that dividing 18 by 2 gives us 9.

### Conclusion
Thus, the missing number in the series is:
\[ \boxed{18} \]