Answer:
HCF of 12, 24 and 36 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.
HCF(12, 24, 36) = HCF(HCF(12, 24), 36)
Steps for HCF(12, 24):
HCF(24, 12) = HCF(12, 24 mod 12) = HCF(12, 0)
HCF(12, 0) = 12 (∵ HCF(X, 0) = |X|, where X ≠ 0)
⇒ HCF(12, 24) = 12
⇒ HCF(HCF(12, 24), 36) = HCF(12, 36)
Steps for HCF(12, 36):
HCF(36, 12) = HCF(12, 36 mod 12) = HCF(12, 0)
HCF(12, 0) = 12 (∵ HCF(X, 0) = |X|, where X ≠ 0)
⇒ HCF(12, 36) = 12
Therefore, the value of HCF of 12, 24, and 36 is 12.
