Answer :

Final answer:

The Highest Common Factor (H.C.F) of 110 and 170 is found using the long division method, resulting in an H.C.F of 10.

Explanation:

To find the Highest Common Factor (H.C.F) of the numbers 110 and 170 using the long division method, we follow the steps below:

  1. Divide the larger number by the smaller number and find the remainder. In this case, divide 170 by 110.
  2. Now divide the divisor (which was 110) by the remainder obtained in the first step. So, we divide 110 by the remainder of the first division.
  3. Continue this process of dividing the previous divisor by the previous remainder until the remainder is 0. The divisor that gives a remainder of 0 is the H.C.F of the given numbers.

Applying this method:

  1. 170 ÷ 110 gives a remainder of 60 (170 = 1×110 + 60).
  2. Now, divide 110 by 60, which gives a remainder of 50 (110 = 1×60 + 50).
  3. Next, divide 60 by 50, which gives a remainder of 10 (60 = 1×50 + 10).
  4. Finally, divide 50 by 10, which gives a remainder of 0 (50 = 5×10 + 0).

Since we've arrived at a remainder of 0, the last non-zero remainder (10) is the H.C.F of 110 and 170.

Therefore, the H.C.F of 110 and 170 is 10.

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Rewritten by : Barada