Find the HCF of 750, 6300, 18900.

Answer

To find the HCF (Highest Common Factor) of the numbers 750, 6300, and 18900 using the continuous division method, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Numbers**: We have three numbers: 750, 6300, and 18900.

2. **Find HCF of the First Two Numbers**: Start by finding the HCF of the first two numbers, which are 6300 and 18900.
- Divide 18900 by 6300.
- \( 18900 \div 6300 = 3 \) (since \( 6300 \times 3 = 18900 \))
- Remainder = 0.
- Since the remainder is 0, the HCF of 6300 and 18900 is 6300.

3. **Use the Result to Find HCF with the Third Number**: Now, we need to find the HCF of 6300 (the result from the previous step) and 750.
- Divide 6300 by 750.
- \( 6300 \div 750 = 8 \) (since \( 750 \times 8 = 6000 \))
- Remainder = \( 6300 - 6000 = 300 \).

4. **Continue the Division**: Now, take the divisor (750) and the remainder (300) and repeat the process.
- Divide 750 by 300.
- \( 750 \div 300 = 2 \) (since \( 300 \times 2 = 600 \))
- Remainder = \( 750 - 600 = 150 \).

5. **Repeat Again**: Now, take 300 and 150.
- Divide 300 by 150.
- \( 300 \div 150 = 2 \) (since \( 150 \times 2 = 300 \))
- Remainder = \( 300 - 300 = 0 \).

6. **Final Result**: Since the last remainder is 0, the HCF is the last non-zero remainder, which is 150.

### Conclusion:
The HCF of 750, 6300, and 18900 is **150**.

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