Question

Find the unit digit of \(13 \times 27 \times 63 \times 51 \times 98 \times 46\).

• A. 4
• B. 8
• C. 2
• D. None of the above

Hint:

Only the last digit of each number affects the unit digit of the product.

Answer 1

The Correct Option is A

Step 1: List the unit digits.
$13, 27, 63, 51, 98, 46$ have unit digits $3, 7, 3, 1, 8, 6$.

Step 2: Multiply all six digits together in one go.
$3 \times 7 \times 3 \times 1 \times 8 \times 6 = 3024$. This time we do not reduce after each step, we just multiply everything out first.

Step 3: Take the unit digit of that final product.
$3024$ ends in 4, and since only unit digits decide the unit digit of a product, this has to match the true answer even though the real numbers are far bigger than 3024.

Final Answer:
Reducing at every step or multiplying it all out first, either way the unit digit comes out to 4.
\[ \boxed{4} \]