By using Euclid's algorithm, find the largest number which divides 650 and 1170.

Answer

To find the largest number that divides both 650 and 1170 using Euclid's algorithm, we follow these steps:

### Step-by-Step Solution:

1. **Identify the two numbers**: We have 650 and 1170. Since 1170 is greater than 650, we will start with these two numbers.

2. **Apply Euclid's Division Lemma**:
- We divide the larger number (1170) by the smaller number (650).
- \( 1170 = 650 \times 1 + 520 \)
- Here, 520 is the remainder.

3. **Repeat the process**: Now we take the previous divisor (650) and the remainder (520) and apply the division again.
- \( 650 = 520 \times 1 + 130 \)
- Now, the remainder is 130.

4. **Continue until the remainder is zero**: We now take the last divisor (520) and the last remainder (130).
- \( 520 = 130 \times 4 + 0 \)
- Here, the remainder is 0.

5. **Identify the HCF**: When the remainder becomes zero, the last non-zero remainder (which is 130 in this case) is the HCF (Highest Common Factor) of the two numbers.

### Conclusion:
The largest number which divides both 650 and 1170 is **130**.

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