Answer :

Final answer:

The H.C.F. (Highest Common Factor) of 84 and 144 can be found through the long division method. In successively dividing the larger number by the smaller and continuing until the remainder is zero, the final divisor is the H.C.F. For the numbers 84 and 144, the H.C.F. is 12.

Explanation:

The H.C.F. (Highest Common Factor) of two numbers can be determined using the long division method. In this method, you successively divide the larger number by the smaller number and continue this process until the remainder is zero.

The divisor at this stage will be the H.C.F. of the two numbers. To find the H.C.F. of 84 and 144 using the long division method, let's follow these steps:

  1. Divide 144 (larger number) by 84 (smaller number). The quotient is 1 and the remainder is 60.
  2. Now take 84 (dividend of the previous step) as dividend and 60 (remainder of the previous step) as the divisor. The quotient is 1 and the remainder is 24.
  3. Again, take 60 (dividend of the previous step) as dividend and 24 (remainder of the previous step) as the divisor. The quotient is 2 and the remainder is 12.
  4. Finally, divide 24 by 12. The quotient is 2 and the remainder is 0. Since the remainder is now 0, we stop here. The divisor at this stage (12) is the H.C.F. of 84 and 144.

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