All even numbers from 2 to 78 inclusive, except those ending with 0, are…
2025
All even numbers from 2 to 78 inclusive, except those ending with 0, are multiplied together. What is the rightmost digit (unit digit) of the product?
- A.
0
- B.
9
- C.
8
- D.
6
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Correct answer: D
Correct answer: 6
Numbers considered: In each block of ten, the allowed even unit digits are 2, 4, 6, and 8. Numbers ending in 0 are excluded.
One block: 2 × 4 × 6 × 8 = 384, so the unit digit contributed by one block is 4.
Number of blocks: From 2 to 78, there are 8 such blocks: 2-8, 12-18, ..., 72-78.
Final unit digit: The product has unit digit 4^8. Powers of 4 alternate unit digits 4 and 6, so every even power has unit digit 6.
Therefore, the rightmost digit of the product is 6.