Unit digit of product of first ten prime number is

Options

A. 6
B. 4
C. 2
D. 0

Answer

To find the unit digit of the product of the first ten prime numbers, we can follow these steps:

### Step 1: Identify the first ten prime numbers.
The first ten prime numbers are:
- 2, 3, 5, 7, 11, 13, 17, 19, 23, 29

### Step 2: Multiply the first ten prime numbers.
We need to calculate the product:
\[ 2 \times 3 \times 5 \times 7 \times 11 \times 13 \times 17 \times 19 \times 23 \times 29 \]

### Step 3: Focus on the unit digit.
To find the unit digit of the product, we can observe that:
- The unit digit of a number is affected by the unit digits of the numbers being multiplied.

### Step 4: Identify the contribution of 2 and 5.
Notice that among the first ten prime numbers, we have both 2 and 5.
- When we multiply 2 and 5, we get:
\[ 2 \times 5 = 10 \]
The unit digit of 10 is 0.

### Step 5: Conclude the unit digit of the entire product.
Since the product contains the factors 2 and 5, the entire product will have a unit digit of 0. This is because multiplying any number by 10 results in a unit digit of 0.

### Final Answer:
The unit digit of the product of the first ten prime numbers is **0**.

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