Explanation:

To solve the problem, let's step through the division method to find the HCF:

- Start with two numbers, say A (larger) and B (smaller).

- According to the division method, when you divide A by B, you get a quotient and a remainder.

- The sequence of quotients given is 1, 8, 2, and the last divisor is 105.

Let's break it down:

1. First division: A ÷ B = 1, remainder (R1)

- A = B * 1 + R1

2. Second division: B ÷ R1 = 8, remainder (R2)

- B = R1 * 8 + R2

3. Third division: R1 ÷ R2 = 2, remainder 0

- R1 = R2 * 2 + 0

- Last divisor (R2) is 105.

Thus, R1 = 105 * 2 = 210 and B = 210 * 8 + 105 = 1785. Finally, A = 1 * 1785 + 210 = 1995.

- Sum of the numbers A and B is 1995 + 1785 = 3780.

Checking the options:

- Option 1: 3570

- Option 2: 3885

- Option 3: 3780

- Option 4: 3675

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