Find the HCF of the numbers in each of the following, using the division method :
1965, 2096

Answer

To find the HCF (Highest Common Factor) of the numbers 1965 and 2096 using the division method, follow these steps:

### Step 1: Arrange the Numbers
We will start by arranging the numbers in descending order. Here, 2096 is greater than 1965.

### Step 2: Divide the Larger Number by the Smaller Number
Now, we will divide the larger number (2096) by the smaller number (1965).

\[ 2096 \div 1965 = 1 \quad \text{(quotient)} \]
\[ \text{Remainder} = 2096 - (1965 \times 1) = 2096 - 1965 = 131 \]

### Step 3: Replace the Larger Number
Now, we replace the larger number (2096) with the smaller number (1965) and the smaller number (1965) with the remainder (131).

### Step 4: Repeat the Division
Next, we will divide the new larger number (1965) by the new smaller number (131).

\[ 1965 \div 131 = 15 \quad \text{(quotient)} \]
\[ \text{Remainder} = 1965 - (131 \times 15) = 1965 - 1965 = 0 \]

### Step 5: Conclusion
Since the remainder is now 0, we stop here. The last non-zero remainder is 131, which is the HCF of 1965 and 2096.

\[ \text{HCF} = 131 \]

### Summary of Steps:
1. Divide the larger number by the smaller number.
2. Replace the larger number with the smaller number and the smaller number with the remainder.
3. Repeat the process until the remainder is 0.
4. The last non-zero remainder is the HCF.