Question

use Euclid devision lemma find the hcf of 567and 567??​

Answer 1

Expert Verified

HCF of 693, 567 = 63. Therefore, HCF of 441 and 63 is 63. Therefore, HCF of 441, 567 and 693 is 63

Answer 2

Answer:

The relation between the LCM and HCF of 441, 567 and 693 is given as, HCF(441, 567, 693) = [(441 × 567 × 693) × LCM(441, 567, 693)]/[LCM(441, 567) × LCM (567, 693) × LCM(441, 693)]

⇒ Prime factorization of 441, 567 and 693:

441 = 3 × 3 × 7 × 7

567 = 3 × 3 × 3 × 3 × 7

693 = 3 × 3 × 7 × 11

∴ LCM of (441, 567), (567, 693), (441, 693), and (441, 567, 693) is 3969, 6237, 4851, and 43659 respectively.

Now, LHS = HCF(441, 567, 693) = 63.

And, RHS = [(441 × 567 × 693) × LCM(441, 567, 693)]/[LCM(441, 567) × LCM (567, 693) × LCM(441, 693)] = [(173282571) × 43659]/[3969 × 6237 × 4851]

LHS = RHS = 63.

Hence verified.