Question

Use Euclid’s Division Lemma to find the H.C.F of 60 and 100.​

Answer 1

Answer:

According to Euclid's division lemma

a=bq +r here

a=100, b=60

100=60*1+40

60=40*1+20

40=20*2

•

• • Hcf of 60 and 100 is 20

Answer 2

Question :

Use Euclid’s Division Lemma to find the H.C.F of 60 and 100.

Theory ;

• Euclid's Division Lemma :If a and b a positive integers such that a=bq+r, then every common divisor of a a and b is a common divisor of b and r, and vice versa.

Solution

Given integers are 100 and 60 such that 100>60 .

Applying euclid's division Lemma to 100 and 60 we get;

100=60×1+40 .....(1)

Since the reminder 40≠0 , so we apply the euclid's division Lemma to 60 and 40 ,to get

60=40×1+20 .....(2)

We consider the new divisor 40 and the new reminder 20 and apply division Lemma to get

40=20×2+0 ....(3)

We observe that the reminder at this stage is zero.

Therefore the divisor at this stage i.e 20(or the reminder at the earlier stage ) is the HCF of 60 and 100

${\purple{\boxed{\large{\bold{HCF\:of\:60\:and\:100=20}}}}}$