Question

Use Euclid's division algorithm to find the HCF of (i) 900 and 270 (ii) 196 and 38220 (iii) 1651 and 2032

Answer 1

Given :

• Use Euclid's division algorithm to find the HCF of :-

(i) 900 and 270

(ii) 196 and 38220

(iii) 1651 and 2032

Solution :

Euclid Division Lemma for a & b is ,

⇒ a = bq + r

we need to do this until r becomes zero

where ,

a is biggest number

b is smaller than a

q is quotient when a is divided by b

r is remainder

( i )

$\sf 900=\underline{270}*3+90\\\\\implies \bf 270=\underline{90}*3+0$

So , 90 is HCF of 900 & 270

( ii )

$\bf 38220=\underline{196}*195+0$

So , 196 is HCF of 38220 & 196

( iii )

$\sf 2032=\underline{1651}*1+381\\\\\implies \sf 1651=\underline{381}*4+127\\\\\implies \bf 381=\underline{127}*3+0$

So 127 is HCF of 2032 & 1651

Answer 2

Given :

Use Euclid's division algorithm to find the HCF of :-

(i) 900 and 270

(ii) 196 and 38220

(iii) 1651 and 2032

Solution :

Euclid Division Lemma for a & b is ,

⇒ a = bq + r

we need to do this until r becomes zero

where ,

a is biggest number

b is smaller than a

q is quotient when a is divided by b

r is remainder

( i )

So , 90 is HCF of 900 & 270

( ii )

So , 196 is HCF of 38220 & 196

( iii )

So 127 is HCF of 2032 & 1651