The HCF of 66, 198 and 154 is _____.

Options

A. 44
B. 66
C. 22
D. 33

Answer

To find the HCF (Highest Common Factor) of the numbers 66, 198, and 154, we will follow these steps:

### Step 1: Find the prime factorization of each number.

1. **Prime factorization of 66**:
- 66 can be divided by 2: \(66 ÷ 2 = 33\)
- 33 can be divided by 3: \(33 ÷ 3 = 11\)
- 11 is a prime number.
- So, the prime factorization of 66 is:
\[ 66 = 2 \times 3 \times 11 \]

2. **Prime factorization of 198**:
- 198 can be divided by 2: \(198 ÷ 2 = 99\)
- 99 can be divided by 3: \(99 ÷ 3 = 33\)
- 33 can be divided by 3: \(33 ÷ 3 = 11\)
- 11 is a prime number.
- So, the prime factorization of 198 is:
\[ 198 = 2 \times 3^2 \times 11 \]

3. **Prime factorization of 154**:
- 154 can be divided by 2: \(154 ÷ 2 = 77\)
- 77 can be divided by 7: \(77 ÷ 7 = 11\)
- 11 is a prime number.
- So, the prime factorization of 154 is:
\[ 154 = 2 \times 7 \times 11 \]

### Step 2: Identify the common prime factors.

Now, we look for the common prime factors in all three factorizations:
- From 66: \(2, 3, 11\)
- From 198: \(2, 3^2, 11\)
- From 154: \(2, 7, 11\)

The common prime factors are:
- **2** (present in all three)
- **11** (present in all three)

### Step 3: Multiply the common prime factors to find the HCF.

Now we multiply the common prime factors:
\[ HCF = 2 \times 11 = 22 \]

### Conclusion:

The HCF of 66, 198, and 154 is **22**.

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