What is the long division method of H.C.F.
84 , 144
Answers
Answer:
HCF of 84 and 144 by Long Division
Step 1: Divide 144 (larger number) by 84 (smaller number). Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (84) by the remainder (60). Step 3: Repeat this process until the remainder = 0.
Step-by-step explanation:
HCF of 84 and 144 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.
Step 1: Divide 144 (larger number) by 84 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (84) by the remainder (60).
Step 3: Repeat this process until the remainder = 0.
The corresponding divisor (12) is the HCF of 84 and 144.
HCF of 84 and 144 by Euclidean Algorithm
As per the Euclidean Algorithm, HCF(X, Y) = HCF(Y, X mod Y)
where X > Y and mod is the modulo operator.
Here X = 144 and Y = 84
HCF(144, 84) = HCF(84, 144 mod 84) = HCF(84, 60)
HCF(84, 60) = HCF(60, 84 mod 60) = HCF(60, 24)
HCF(60, 24) = HCF(24, 60 mod 24) = HCF(24, 12)
HCF(24, 12) = HCF(12, 24 mod 12) = HCF(12, 0)
HCF(12, 0) = 12 (∵ HCF(X, 0) = |X|, where X ≠ 0)
Therefore, the value of HCF of 84 and 144 is 12.
☛ Also Check:
HCF of 18, 54 and 81 = 9
HCF of 45 and 180 = 45
HCF of 12 and 30 = 6
HCF of 324 and 144 = 36
HCF of 20, 28 and 36 = 4
HCF of 14 and 15 = 1
HCF of 4052 and 12576 = 4
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