Question

Using Euclid Division Lemma, Find the HCF of
(I) 441, 567 and 62.​

Answer 1

Answer:

The Euclidean Algorithm for finding HCF (A,B) is as follows:

If A=0 then HCF (A,B)=B, since the HCF (0,B)=B, and we can stop.

If B=0 then HCF (A,B)=A, since the HCF (A,0)=A, and we can stop.

Write A in quotient remainder form (A=BQ+R)

Find HCF (B,R) using the Euclidean Algorithm since

HCF (A,B)=HCF(B,R)

Here, HCF of 441 and 567 can be found as follows:-

567=441×1+126

⇒ 441=126×3+63

⇒ 126=63×2+0

Since remainder is 0, therefore,

H.C.F of (441,567) is =63

Now H.C.F of 63 and 693 is

693=63×11+0

Therefore, H.C.F of (63,693)=63

Thus, H.C.F of (441,567,693)=63.