H.C.F of `2^(3), 3^(2)` and 15 is-

Options

A. `2^(3)`
B. `3^(2)`
C. 1
D. 360

Answer

To find the H.C.F (Highest Common Factor) of \(2^3\), \(3^2\), and \(15\), we will follow these steps:

### Step 1: Find the prime factorization of each number.
- \(2^3 = 2 \times 2 \times 2\)
- \(3^2 = 3 \times 3\)
- \(15 = 3 \times 5\)

### Step 2: List the prime factors of each number.
- The prime factors of \(2^3\) are: \(2\)
- The prime factors of \(3^2\) are: \(3\)
- The prime factors of \(15\) are: \(3\) and \(5\)

### Step 3: Identify the common prime factors.
- The only common prime factor among \(2^3\), \(3^2\), and \(15\) is \(1\) (since \(2\) and \(3\) do not appear in all three).

### Step 4: Determine the H.C.F.
- Since the only common factor is \(1\), the H.C.F of \(2^3\), \(3^2\), and \(15\) is \(1\).

### Final Answer:
The H.C.F of \(2^3\), \(3^2\), and \(15\) is \(1\).

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