Find the HCF of 161 and 345 by the division method.

Answer

To find the HCF (Highest Common Factor) of 161 and 345 using the division method, follow these steps:

### Step 1: Identify the larger and smaller numbers
- Here, the larger number is 345 and the smaller number is 161.

### Step 2: Divide the larger number by the smaller number
- Divide 345 by 161.

\[ 345 \div 161 = 2 \quad \text{(quotient)} \]
\[ \text{Remainder} = 345 - (161 \times 2) = 345 - 322 = 23 \]

### Step 3: Replace the numbers
- Now, replace the larger number with the smaller number and the smaller number with the remainder from the previous division. So, we will now divide 161 by 23.

### Step 4: Divide the new pair
- Divide 161 by 23.

\[ 161 \div 23 = 7 \quad \text{(quotient)} \]
\[ \text{Remainder} = 161 - (23 \times 7) = 161 - 161 = 0 \]

### Step 5: Determine the HCF
- Since the remainder is now 0, the divisor from the last division (which is 23) is the HCF of 161 and 345.

### Final Answer:
- The HCF of 161 and 345 is **23**.

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