Find the HCF of 527, 1020 and 11594 :

Question

Accepted Answer

To find the Highest Common Factor (HCF) of the numbers 527, 1020, and 11594, we need to determine the largest number that divides all three numbers without leaving a remainder. The correct answer is Option 3, which is 17. Here is a detailed explanation:

1. **Prime Factorization Method:**
   - **527:** The prime factorization of 527 is 17 × 31.
   - **1020:** The prime factorization of 1020 is 2 × 2 × 3 × 5 × 17.
   - **11594:** The prime factorization of 11594 is 2 × 7 × 829.

From the prime factorizations, we can see that the number 17 is a common factor of both 527 and 1020. However, 17 is not a factor of 11594. Therefore, we need to verify the divisibility of 11594 by 17.

2. **Verification of Divisibility:**
   - **11594 ÷ 17 = 682** (exact division with no remainder)

Since 17 divides all three numbers (527, 1020, and 11594) exactly, it is the HCF.

3. **Explanation of Incorrect Options:**
   - **Option 1 (13):** The number 13 is not a factor of any of the given numbers (527, 1020, or 11594) based on their prime factorizations.
   - **Option 2 (14):** The number 14 is not a factor of any of the given numbers. It is composed of the prime factors 2 and 7, neither of which is a common factor of all three numbers.
   - **Option 4 (19):** The number 19 is not a factor of any of the given numbers based on their prime factorizations.

Therefore, the correct answer is Option 3, which is 17, as it is the largest number that divides all three numbers without leaving a remainder.