Identify the HCF of the numbers 15, 30 and 52 among the options.

Options

A. 1
B. 30
C. 2
D. 15

Answer

To find the Highest Common Factor (HCF) of the numbers 15, 30, and 52, we will follow these steps:

### Step 1: Factor each number into its prime factors.
- **For 15**: The prime factorization of 15 is \( 3 \times 5 \).
- **For 30**: The prime factorization of 30 is \( 2 \times 3 \times 5 \).
- **For 52**: The prime factorization of 52 is \( 2 \times 2 \times 13 \) or \( 2^2 \times 13 \).

### Step 2: List the prime factors.
- Factors of 15: \( 3, 5 \)
- Factors of 30: \( 2, 3, 5 \)
- Factors of 52: \( 2, 2, 13 \)

### Step 3: Identify the common factors.
Now we will look for the common prime factors among the three numbers:
- The prime factor \( 3 \) is present in 15 and 30 but not in 52.
- The prime factor \( 5 \) is present in 15 and 30 but not in 52.
- The prime factor \( 2 \) is present in 30 and 52 but not in 15.

### Step 4: Determine the HCF.
Since there are no prime factors that are common to all three numbers, the only common factor is \( 1 \).

### Conclusion:
Thus, the HCF of 15, 30, and 52 is \( 1 \).

### Final Answer:
The correct option is \( 1 \).

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