Find the unit digit in the product of `(268 xx 589 xx 826 xx 102).`

Options

A. 2
B. 3
C. 4
D. 5

Answer

To find the unit digit in the product of \( 268 \times 589 \times 826 \times 102 \), we can follow these steps:

### Step 1: Identify the Unit Digits
First, we need to find the unit digit of each number in the product:
- The unit digit of \( 268 \) is \( 8 \).
- The unit digit of \( 589 \) is \( 9 \).
- The unit digit of \( 826 \) is \( 6 \).
- The unit digit of \( 102 \) is \( 2 \).

### Step 2: Multiply the Unit Digits
Now, we will multiply these unit digits together:
\[ 8 \times 9 \times 6 \times 2 \]

### Step 3: Calculate \( 8 \times 9 \)
First, we calculate \( 8 \times 9 \):
\[ 8 \times 9 = 72 \]
The unit digit of \( 72 \) is \( 2 \).

### Step 4: Multiply the Result with the Next Unit Digit
Next, we multiply the unit digit \( 2 \) (from \( 72 \)) with \( 6 \):
\[ 2 \times 6 = 12 \]
The unit digit of \( 12 \) is \( 2 \).

### Step 5: Multiply the Result with the Last Unit Digit
Now, we multiply the unit digit \( 2 \) (from \( 12 \)) with \( 2 \):
\[ 2 \times 2 = 4 \]
The unit digit of \( 4 \) is \( 4 \).

### Conclusion
Thus, the unit digit in the product \( 268 \times 589 \times 826 \times 102 \) is \( 4 \).

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