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

1.	Use Euclid's division algorithm to find the HCF of(i) 900 and 270(ii) 196 and 38220(iii)I651 and 2032
Answer» 1)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

Use Euclid's division algorithm to find the HCF of(i) 900 and 270(ii) 196 and 38220(iii)I651 and 2032

Answer»

1)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