Q. 154.5( 8 Votes )

Find the HCF of 1620 1725 and 255 by Euclid’s division algorithm.

Answer :

We know Euclid's division lemma:

Let a and b be any two positive integers. Then there exist two unique whole numbers q and r such that


a = b q + r,


where 0 ≤ r < b


Here, a is called the dividend,


b is called the divisor,


q is called the quotient and


r is called the remainder.


According to the problem given,


Let’s start with 1620 and 1725.


Apply the division lemma on 1725 and 1620,


1725 = (1620 × 1) + 105


Since the remainder is not equal to zero,


Apply lemma again on 1620 and 105. We get,


1620 = (105 × 15) + 45


Since the remainder is not equal to zero, apply lemma again on 105 and 45. We get,


105 = (45 × 2) + 15


Since the remainder is not equal to zero, apply lemma again on 45 and 15. We get,


45 = (15 × 3) + 0


The remainder has now become zero.


HCF (1620, 1725) = 15


Now we have to find HCF of 255 and 15.


Similarly, apply lemma on 225 and 15.


We get,


225 = (15 × 15) + 0


Since, the remainder is equal to 0.


HCF (225, 15) = 15


Therefore, HCF (1620, 1725, 225) = 15.


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