Find the H.C.F of 36 , 96 and 120 by Euclid\'s division lemma

1.	Find the H.C.F of 36 , 96 and 120 by Euclid\'s division lemma
Answer» Euclid\'s division algorithm is to compute the highest common factor (HCF) of two or three given positive integers.Euclid\'s division lemma states that for any two positive integers say a and b there exists two unique whole number say q and r , such that ,a =b q+r , where 0 ‹ r ‹b.Solution : on applying Euclid\'s division lemma for 36 and 96 96 = 36 ×2 +24Here , remainder = 24≠0 So take new dividend as 36 and divisor as 24.36=24×1+12Here,the remainder=12≠0So,take new dividend as 24 and divisor as 12.24=12×10+0Here,the Remainder=0 and the last divisor is 12 .So, HCF of 36 and 96 is 12.On applying Euclid\'s division lemma for 12 and 120 120=12×10+0Here remainder=0So ,HCF of 36,96 and 120 = 12.

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