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

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,

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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