Find the HCF and LCM of
2923, 3239

Answer

To find the HCF (Highest Common Factor) and LCM (Lowest Common Multiple) of the numbers 2923 and 3239, we can follow these steps:

### Step 1: Find the HCF using the Division Method

1. **Divide the larger number by the smaller number**:
- Divide 3239 by 2923.
- \( 3239 \div 2923 = 1 \) (quotient) with a remainder of \( 3239 - 2923 = 316 \).

2. **Now, divide the previous divisor by the remainder**:
- Divide 2923 by 316.
- \( 2923 \div 316 = 9 \) (quotient) with a remainder of \( 2923 - (316 \times 9) = 2923 - 2844 = 79 \).

3. **Continue this process**:
- Now, divide the previous divisor (316) by the new remainder (79).
- \( 316 \div 79 = 4 \) (quotient) with a remainder of \( 316 - (79 \times 4) = 316 - 316 = 0 \).

4. **When the remainder is 0, the last non-zero remainder is the HCF**:
- The last non-zero remainder is 79.
- Therefore, **HCF(2923, 3239) = 79**.

### Step 2: Find the LCM using the relationship between HCF and LCM

1. **Use the formula**:
- The relationship between HCF and LCM is given by:
\[ \text{HCF} \times \text{LCM} = \text{Product of the two numbers} \]
- In this case:
\[ \text{LCM} = \frac{\text{Product of the two numbers}}{\text{HCF}} \]

2. **Calculate the product of the two numbers**:
- \( 2923 \times 3239 = 946,837 \).

3. **Now substitute the values into the formula**:
- Using the HCF we found (79):
\[ \text{LCM} = \frac{946,837}{79} \]

4. **Calculate the LCM**:
- \( 946,837 \div 79 = 11,999 \).
- Therefore, **LCM(2923, 3239) = 11,999**.

### Final Answer:
- HCF of 2923 and 3239 is **79**.
- LCM of 2923 and 3239 is **11,999**.

---