Find the HCF of numbers 134791, 6341 and 6339 by Euclid's division algorithm.

Answer

To find the HCF (Highest Common Factor) of the numbers 134791, 6341, and 6339 using Euclid's division algorithm, we will follow these steps:

### Step 1: Find HCF of 6341 and 6339
We will start by applying Euclid's division algorithm to the two numbers 6341 and 6339.

1. **Divide 6341 by 6339:**
\[ 6341 = 6339 \times 1 + 2 \]
Here, the quotient (Q) is 1 and the remainder (R) is 2.

### Step 2: Use the remainder to find HCF
Now we will use the remainder (2) and divide the smaller number (6339) by this remainder.

2. **Divide 6339 by 2:**
\[ 6339 = 2 \times 3169 + 1 \]
Here, the quotient is 3169 and the remainder is 1.

### Step 3: Continue with the new remainder
Now we will divide the previous remainder (2) by the new remainder (1).

3. **Divide 2 by 1:**
\[ 2 = 1 \times 2 + 0 \]
Here, the quotient is 2 and the remainder is 0.

### Step 4: Conclusion for HCF of 6341 and 6339
Since the remainder is now 0, we conclude that the HCF of 6341 and 6339 is the last non-zero remainder, which is 1.

### Step 5: Find HCF of the result with the third number
Now we need to find the HCF of the result (1) and the third number (134791).

4. **Divide 134791 by 1:**
\[ 134791 = 1 \times 134791 + 0 \]
Here, the quotient is 134791 and the remainder is 0.

### Step 6: Conclusion for HCF of all three numbers
Since the remainder is 0, we conclude that the HCF of 134791, 6341, and 6339 is the last non-zero remainder, which is 1.

### Final Answer
The HCF of the numbers 134791, 6341, and 6339 is **1**.

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