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

Objective:
Determine which digit *cannot* be the units digit of 8ⁿ, where *n* is a positive integer.

Analysis: Units Digits of Powers of 8
Calculate the first few powers of 8:
8¹ = 8 (units digit: 8)
8² = 64 (units digit: 4)
8³ = 512 (units digit: 2)
8⁴ = 4096 (units digit: 6)
8⁵ = 32768 (units digit: 8)
8⁶ = 262144 (units digit: 4)
8⁷ = 2097152 (units digit: 2)
8⁸ = 16777216 (units digit: 6)

Pattern Recognition
The units digit repeats in the sequence: 8, 4, 2, 6.

Deduction
The units digit of 8ⁿ must be one of: 8, 4, 2, or 6.
Therefore, any other digit (0, 1, 3, 5, 7, or 9) is impossible.

Answer:
0 is not a possible units digit for 8ⁿ.