Find out the unit digit in the product of all the even numbers.

Options

A. a) 5
B. b) 2
C. c) 0
D. d) 4

Answer

To find the unit digit in the product of all even numbers, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Even Numbers**:
The sequence of even numbers starts from 2 and continues indefinitely: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, ...

2. **Understanding the Product**:
We need to find the product of all these even numbers. However, we are only interested in the unit digit of this product.

3. **Focus on the Unit Digits**:
The unit digits of the even numbers are:
- 2 (from 2)
- 4 (from 4)
- 6 (from 6)
- 8 (from 8)
- 0 (from 10)
- 2 (from 12)
- 4 (from 14)
- 6 (from 16)
- 8 (from 18)
- 0 (from 20)
- And so on...

4. **Notice the Presence of 0**:
In the sequence of even numbers, we can see that 10 is included, which has a unit digit of 0.

5. **Conclusion**:
When we multiply any number by 0, the result is always 0. Therefore, since the product of all even numbers includes the number 10 (which contributes a unit digit of 0), the unit digit of the entire product will also be 0.

### Final Answer:
The unit digit in the product of all even numbers is **0**.

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