In finding the HCF of two numbers by division method, the quotients are 1, 8 and 2 respectively, and the last divisor is 105. What is the sum of the numbers?

Working backwards through the Euclidean division algorithm with the last divisor of 105 and a final quotient of 2, the previous dividend is calculated as 105 times 2 plus a remainder of 0, giving 210. Using 105 and 210 with the previous quotient of 8, the next dividend is 210 times 8 plus 105, which is 1785. For the first step using the quotient 1, the original larger number is 1785 times 1 plus 210, which equals 1995. The two original numbers are 1995 and 1785, and their sum is 3780.

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