Write the H.C.F. of the smallest composite number and the smallest prime number.

Answer

To find the H.C.F. (Highest Common Factor) of the smallest composite number and the smallest prime number, we can follow these steps:

### Step 1: Identify the smallest prime number.
- A prime number is defined as a number that has exactly two distinct positive divisors: 1 and itself.
- The smallest prime number is **2**.

### Step 2: Identify the smallest composite number.
- A composite number is defined as a number that has more than two distinct positive divisors.
- The smallest composite number is **4** (since its divisors are 1, 2, and 4).

### Step 3: Find the prime factorization of both numbers.
- The prime factorization of **2** is:
\[ 2 = 2^1 \]
- The prime factorization of **4** is:
\[ 4 = 2^2 \]

### Step 4: Determine the H.C.F. of the two numbers.
- To find the H.C.F., we take the lowest power of all prime factors common to both numbers.
- The common prime factor is **2**.
- The lowest power of 2 in the factorizations is \(2^1\).

### Step 5: Write the final answer.
- Therefore, the H.C.F. of the smallest composite number (4) and the smallest prime number (2) is:
\[ \text{H.C.F.} = 2 \]