Question

Use Euclid Division algorithm to find the HCF of 1620,225,1725.

Answer 1

Euclid's division lemma:

Let a and b be any two positive integers.

Then there exists two unique whole numbers q such that

a = bq + r ,

Where 0 less or equal to zero r < b

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According to the problem given,

First find the HCF of 1620 and 1725

1725 = 1620 × 1 + 105

1620 = 105 × 15 + 45

105 = 45 × 2 + 15

45 = 15 × 3 + 0

HCF ( 1725 , 1620 ) = 15

Now we have to find HCF of 15 and 255

255 = 15 × 17 + 0

HCF ( 15 , 255 ) = 15

Therefore ,

HCF ( 1620 , 1725 , 255 ) = 15

I hope this will help you.