Question

Which of the following cannot be the unit digit of $8^n$, where $n$ is a natural number?

• A. 4
• B. 2
• C. 0
• D. 6

Hint:

Learn the unit digit cycles of powers for common numbers.

Answer 1

The Correct Option is C

To Find:
Which of the following cannot be the unit digit of 8ⁿ, where n is a natural number?

Step 1: Observe the unit digits of powers of 8
Let's compute the first few powers of 8:
8¹ = 8 → unit digit = 8
8² = 64 → unit digit = 4
8³ = 512 → unit digit = 2
8⁴ = 4096 → unit digit = 6
8⁵ = 32768 → unit digit = 8
8⁶ = 262144 → unit digit = 4
8⁷ = 2097152 → unit digit = 2
8⁸ = 16777216 → unit digit = 6

Step 2: Identify the repeating pattern
The unit digit repeats in a cycle: 8, 4, 2, 6

Step 3: Conclusion
The unit digit of 8ⁿ can only be one of: 8, 4, 2, or 6
So any other digit, such as 0, 1, 3, 5, 7, or 9, cannot be a unit digit of 8ⁿ

Final Answer:
0 cannot be the unit digit of 8ⁿ