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Answer :
To find the highest common factor using long division, divide the given numbers until the remainder is 0. The divisor at this point will be the H.C.F.
To find the H.C.F (Highest Common Factor) using the long division method, we divide the given numbers and continue dividing until we get a remainder of 0.
The divisor at this point will be the H.C.F.
Let's solve each part of the question:
a. For 84 and 144, we divide 144 by 84 and get a quotient of 1 and remainder 60. We then divide 84 by 60 and get a quotient of 1 and remainder 24.
We continue dividing until we get a remainder of 0. Therefore, the H.C.F of 84 and 144 is 12.
b. For 120 and 168, we divide 168 by 120 and get a quotient of 1 and remainder 48.
We then divide 120 by 48 and get a quotient of 2 and remainder 24. We continue dividing until we get a remainder of 0.
Therefore, the H.C.F of 120 and 168 is 24.
c. For 430, 516, and 817, we divide 516 by 430 and get a quotient of 1 and remainder 86.
We then divide 430 by 86 and get a quotient of 5 and remainder 0.
Therefore, the H.C.F of 430, 516, and 817 is 86.
d. For 632, 790, and 869, we divide 790 by 632 and get a quotient of 1 and remainder 158.
We then divide 632 by 158 and get a quotient of 4 and remainder 0.
Therefore, the H.C.F of 632, 790, and 869 is 158.
e. For 291, 582, and 776, we divide 582 by 291 and get a quotient of 2 and remainder 0.
Therefore, the H.C.F of 291, 582, and 776 is 291.
f. For 219, 1321, 2320, and 8526, we divide 1321 by 219 and get a quotient of 6 and remainder 157. We then divide 219 by 157 and get a quotient of 1 and remainder 62.
We divide 157 by 62 and get a quotient of 2 and remainder 33. We divide 62 by 33 and get a quotient of 1 and remainder 29.
We divide 33 by 29 and get a quotient of 1 and remainder 4. We divide 29 by 4 and get a quotient of 7 and remainder 1.
We divide 4 by 1 and get a quotient of 4 and remainder 0. Therefore, the H.C.F of 219, 1321, 2320, and 8526 is 1.
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