The HCF of first `100` natural numbers is:

Options

A. `2`
B. `100`
C. `1`
D. None of these

Answer

To find the HCF (Highest Common Factor) of the first 100 natural numbers, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the First 100 Natural Numbers**:
The first 100 natural numbers are:
\[ 1, 2, 3, 4, 5, \ldots, 100 \]

2. **Understand the Concept of HCF**:
The HCF of a set of numbers is the largest number that divides all of them without leaving a remainder.

3. **Recognize the Nature of the Numbers**:
The first 100 natural numbers include consecutive integers. For example, 1, 2, 3, 4, ..., 100 are all consecutive.

4. **Apply the Rule for Consecutive Numbers**:
The HCF of any two consecutive numbers is always 1. This is because consecutive numbers have no common factors other than 1. For instance:
- HCF(1, 2) = 1
- HCF(2, 3) = 1
- HCF(3, 4) = 1
- And so on.

5. **Extend the Rule to 100 Numbers**:
Since the first 100 natural numbers are all consecutive, the HCF of all these numbers will also be 1.

6. **Conclusion**:
Therefore, the HCF of the first 100 natural numbers is:
\[ \text{HCF} = 1 \]

### Final Answer:
The HCF of the first 100 natural numbers is **1**.

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