Find the HCF of 527 , 1020 and 11594.

Options

A. 13
B. 14
C. 17
D. 19

Answer

To find the HCF (Highest Common Factor) of the numbers 527, 1020, and 11594, we can follow these steps:

### Step 1: Find the differences between the numbers
First, we can calculate the differences between the numbers to simplify our calculations.

- Difference between 1020 and 527:
\[ 1020 - 527 = 493 \]

- Difference between 11594 and 1020:
\[ 11594 - 1020 = 10574 \]

### Step 2: Check for divisibility
Next, we need to check if 493 divides the other numbers. We can start with 527 and 1020.

- Check if 493 divides 527:
\[ 527 \div 493 = 1.069 \quad (\text{not an integer, so 493 does not divide 527}) \]

- Check if 493 divides 1020:
\[ 1020 \div 493 = 2.067 \quad (\text{not an integer, so 493 does not divide 1020}) \]

Since 493 does not divide either number, we need to find the prime factors of 493.

### Step 3: Factor 493
We can check for prime factors of 493.

- Check divisibility by 13:
\[ 493 \div 13 = 37.1538 \quad (\text{not an integer}) \]

- Check divisibility by 17:
\[ 493 \div 17 = 29 \quad (\text{is an integer, so 493 = 17 × 29}) \]

### Step 4: Check divisibility of the original numbers by 17
Now we will check if 17 divides each of the original numbers.

- Check if 17 divides 527:
\[ 527 \div 17 = 31 \quad (\text{is an integer}) \]

- Check if 17 divides 1020:
\[ 1020 \div 17 = 60 \quad (\text{is an integer}) \]

- Check if 17 divides 11594:
\[ 11594 \div 17 = 682 \quad (\text{is an integer}) \]

### Conclusion
Since 17 divides all three numbers exactly, we conclude that the HCF of 527, 1020, and 11594 is:
\[ \text{HCF} = 17 \]