Find the HCF of 143, 77 and 121.

Options

A. 6
B. 11
C. 4
D. 7

Answer

To find the HCF (Highest Common Factor) of the numbers 143, 77, and 121, we can follow these steps:

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

1. **Prime Factorization of 143:**
- Divide 143 by the smallest prime number, which is 11.
- 143 ÷ 11 = 13
- Therefore, the prime factorization of 143 is:
\[ 143 = 11 \times 13 \]

2. **Prime Factorization of 77:**
- Divide 77 by the smallest prime number, which is 7.
- 77 ÷ 7 = 11
- Therefore, the prime factorization of 77 is:
\[ 77 = 7 \times 11 \]

3. **Prime Factorization of 121:**
- Divide 121 by the smallest prime number, which is 11.
- 121 ÷ 11 = 11
- Therefore, the prime factorization of 121 is:
\[ 121 = 11 \times 11 \quad \text{or} \quad 11^2 \]

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

Now we have the prime factorizations:
- 143 = 11 × 13
- 77 = 7 × 11
- 121 = 11 × 11

The common prime factor in all three numbers is **11**.

### Step 3: Determine the HCF.

The HCF is the product of the lowest powers of all common prime factors. Since 11 is the only common prime factor, the HCF is:
\[ \text{HCF} = 11 \]

### Conclusion:
The HCF of 143, 77, and 121 is **11**.

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