Use Euclid's algorithm to find the HCF(i) 900 and 270 ii) 196 and 382

1.	Use Euclid's algorithm to find the HCF(i) 900 and 270 ii) 196 and 382
Answer» 1)Euclid's division lemma : Let a and b be any two positive integers .Then there exists two unique whole numbers q and r such that a = bq + r , 0 ≤ r < b ****************************************** Now , 900 and 270 , start with the larger integer , that is 900. Apply the Division lemma , we get 900 = 270 × 3 + 90 270 = 90 × 3 + 0 The remainder has now become zero . Now our procedure stops. Since the divisor at this stage is 90. Therefore , HCF ( 900 , 270 ) = 90

Answer»

1)Euclid's division lemma :

Let a and b be any two positive

integers .Then there exists two

unique whole numbers q and r

such that

a = bq + r ,

0 ≤ r < b

******************************************

Now ,

900 and 270 , start with the larger

integer , that is 900. Apply the

Division lemma , we get

900 = 270 × 3 + 90

270 = 90 × 3 + 0

The remainder has now become

zero . Now our procedure stops.

Since the divisor at this stage is 90.

Therefore ,

HCF ( 900 , 270 ) = 90

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