41472 5184 576 72 8 ?

Options

A. 0
B. 9
C. 1
D. 8

Explanation

To solve the series: 41472, 5184, 576, 72, 8, ?, we need to identify the pattern in the numbers.

### Step-by-Step Solution:

1. **Identify the Series**: The series is as follows:
- 41472
- 5184
- 576
- 72
- 8
- ?

2. **Observe the Pattern**: Notice that the numbers are decreasing significantly. This suggests that we might be dividing by a certain number or multiplying by a fraction.

3. **Calculate the Division**:
- Let's start with the last two numbers:
- \( 72 \div 8 = 9 \)
- This suggests that the previous number (72) is obtained by multiplying 8 by 9.

4. **Continue the Pattern**:
- Now, let's check the next pair:
- \( 576 \div 72 = 8 \)
- This means that 576 is obtained by multiplying 72 by 8.

5. **Next Pair**:
- Now, check the next pair:
- \( 5184 \div 576 = 9 \)
- This means that 5184 is obtained by multiplying 576 by 9.

6. **Final Pair**:
- Now, check the first pair:
- \( 41472 \div 5184 = 8 \)
- This means that 41472 is obtained by multiplying 5184 by 8.

7. **Identify the Pattern**:
- From the calculations, we see that the pattern alternates between multiplying by 9 and multiplying by 8:
- \( 41472 \) to \( 5184 \) (divide by 8)
- \( 5184 \) to \( 576 \) (divide by 9)
- \( 576 \) to \( 72 \) (divide by 8)
- \( 72 \) to \( 8 \) (divide by 9)

8. **Determine the Next Number**:
- Following the established pattern, the next number should be obtained by multiplying 8 by 9:
- \( 8 \times 9 = 72 \)

9. **Final Answer**: The next number in the series is **1** (since \( 1 \times 8 = 8 \)).

### Summary of the Steps:
1. Identify the series.
2. Observe the pattern of division.
3. Calculate the division for each pair.
4. Identify the alternating multiplication pattern of 8 and 9.
5. Calculate the next number using the established pattern.