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

To find the unit digit of the product \(13 \times 27 \times 63 \times 51 \times 98 \times 46\), we need to focus only on the unit digits of each of these numbers individually, as the unit digit of a product depends solely on the unit digits of the numbers involved.

1. The unit digit of \(13\) is \(3\). 
2. The unit digit of \(27\) is \(7\).
3. The unit digit of \(63\) is \(3\).
4. The unit digit of \(51\) is \(1\).
5. The unit digit of \(98\) is \(8\).
6. The unit digit of \(46\) is \(6\).

Now, we calculate the unit digit of the product of these unit digits: \(3 \times 7 \times 3 \times 1 \times 8 \times 6\).

1. \(3 \times 7 = 21\) (unit digit is \(1\))
2. \(1 \times 3 = 3\) (unit digit is \(3\))
3. \(3 \times 1 = 3\) (unit digit is \(3\))
4. \(3 \times 8 = 24\) (unit digit is \(4\))
5. \(4 \times 6 = 24\) (unit digit is \(4\))

Thus, the unit digit of the product of all these numbers is \(4\).

Therefore, the correct option is 4.

Answer 2

Step 1: Pick out the unit digit of each number.
Only the last digit of each number decides the unit digit of the product. The unit digits here are 3 (from 13), 7 (from 27), 3 (from 63), 1 (from 51), 8 (from 98), and 6 (from 46).

Step 2: Multiply the unit digits one pair at a time.
\(3 \times 7 = 21\), keep the unit digit 1.
\(1 \times 3 = 3\), unit digit 3.
\(3 \times 1 = 3\), unit digit 3.
\(3 \times 8 = 24\), unit digit 4.
\(4 \times 6 = 24\), unit digit 4.

Step 3: Read off the final unit digit.
After multiplying all six unit digits step by step, the last digit left standing is 4.

Final Answer:
The unit digit of the product is 4.
\[ \boxed{4} \]