The unit digit of `71xx72xx.....xx79` is

Options

A. a)0
B. b)4
C. c)6
D. d)7

Answer

To find the unit digit of the product \(71 \times 72 \times 73 \times 74 \times 75 \times 76 \times 77 \times 78 \times 79\), we can follow these steps:

### Step 1: Identify the unit digits
First, we need to identify the unit digits of each number in the product:
- The unit digit of 71 is **1**
- The unit digit of 72 is **2**
- The unit digit of 73 is **3**
- The unit digit of 74 is **4**
- The unit digit of 75 is **5**
- The unit digit of 76 is **6**
- The unit digit of 77 is **7**
- The unit digit of 78 is **8**
- The unit digit of 79 is **9**

### Step 2: Write down the unit digits
Now, we can write down the unit digits:
\[ 1, 2, 3, 4, 5, 6, 7, 8, 9 \]

### Step 3: Calculate the product of the unit digits
Next, we will multiply these unit digits together:
\[ 1 \times 2 \times 3 \times 4 \times 5 \times 6 \times 7 \times 8 \times 9 \]

### Step 4: Recognize the presence of 5 and even numbers
Notice that in the product, we have the digit **5** and even numbers (2, 4, 6, 8). The presence of **5** and an even number guarantees that the product will include a factor of **10**.

### Step 5: Conclusion about the unit digit
Since the product contains a factor of **10**, the unit digit of the entire product will be **0**.

### Final Answer
Thus, the unit digit of \(71 \times 72 \times 73 \times 74 \times 75 \times 76 \times 77 \times 78 \times 79\) is **0**.

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