H.C.F. (726, 275) is equal to:

Question

Accepted Answer

To determine the H.C.F. (Highest Common Factor) of the numbers 726 and 275, we need to find the largest number that divides both 726 and 275 without leaving a remainder. The correct answer is given as Option 4, which is 11. Let's go through the explanation to support this answer.

### Explanation:

1. **Prime Factorization Method:**
   - First, we perform the prime factorization of each number.
   - **726:** 
     - 726 is an even number, so it is divisible by 2: 
       - $ 726 \div 2 = 363 $
     - 363 is divisible by 3 (since the sum of its digits, 3 + 6 + 3 = 12, is divisible by 3):
       - $ 363 \div 3 = 121 $
     - 121 is a perfect square of 11:
       - $ 121 = 11 \times 11 $
     - Therefore, the prime factorization of 726 is $ 2 \times 3 \times 11 \times 11 $.

- **275:**
     - 275 is not divisible by 2 or 3, but it ends in 5, so it is divisible by 5:
       - $ 275 \div 5 = 55 $
     - 55 is divisible by 5 and 11:
       - $ 55 = 5 \times 11 $
     - Therefore, the prime factorization of 275 is $ 5 \times 11 $.

2. **Finding the H.C.F.:**
   - The common prime factor between 726 and 275 is 11.
   - Therefore, the H.C.F. of 726 and 275 is 11.

### Why Other Options are Incorrect:

- **Option 1 (55):** 
  - 55 is a factor of 275 but not a factor of 726. Therefore, it cannot be the H.C.F.

- **Option 2 (33):**
  - 33 is not a factor of 275 (since 275 is not divisible by 3). Therefore, it cannot be the H.C.F.

- **Option 3 (22):**
  - 22 is not a factor of 275 (since 275 is not divisible by 2). Therefore, it cannot be the H.C.F.

Thus, the correct answer is Option 4, which is 11, as it is the largest number that divides both 726 and 275 without leaving a remainder.