The HCF of 252 and 308 is :

Options

A. 4
B. 12
C. 14
D. 28

Answer

To find the HCF (Highest Common Factor) of 252 and 308, we will use the prime factorization method. Here are the steps to solve the problem:

### Step 1: Prime Factorization of 252
To find the prime factors of 252, we start dividing by the smallest prime number, which is 2.

1. **Divide by 2:**
\[ 252 \div 2 = 126 \]
2. **Divide by 2 again:**
\[ 126 \div 2 = 63 \]
3. **Now, divide by the next smallest prime number, which is 3:**
\[ 63 \div 3 = 21 \]
4. **Divide by 3 again:**
\[ 21 \div 3 = 7 \]
5. **Finally, 7 is a prime number.**

So, the prime factorization of 252 is:
\[ 252 = 2^2 \times 3^2 \times 7^1 \]

### Step 2: Prime Factorization of 308
Now, we will find the prime factors of 308.

1. **Divide by 2:**
\[ 308 \div 2 = 154 \]
2. **Divide by 2 again:**
\[ 154 \div 2 = 77 \]
3. **Now, divide by the next smallest prime number, which is 7:**
\[ 77 \div 7 = 11 \]
4. **Finally, 11 is a prime number.**

So, the prime factorization of 308 is:
\[ 308 = 2^2 \times 7^1 \times 11^1 \]

### Step 3: Identify Common Factors
Now, we will identify the common factors from the prime factorizations of both numbers.

- For 252: \(2^2 \times 3^2 \times 7^1\)
- For 308: \(2^2 \times 7^1 \times 11^1\)

The common prime factors are:
- \(2^2\) (the minimum power of 2 in both factorizations)
- \(7^1\) (the minimum power of 7 in both factorizations)

### Step 4: Calculate the HCF
Now, we multiply the common factors to find the HCF:
\[ \text{HCF} = 2^2 \times 7^1 = 4 \times 7 = 28 \]

Thus, the HCF of 252 and 308 is **28**.