Explanation
If p=d×q+r, (p>q) where p, q, d, r are integers and for a given (p, d), there exist a unique (q, r), then HCF (p, d) = HCF (d, r). Because this relation holds true, the Euclid’s Division Algorithm exists in a step by step manner. So, to find the HCF (1008, 20), we use Euclid’s division lemma at every step.
Step 1: 1008=20×50+8 ⇒ HCF(1008, 20) = HCF(20,8) ⇒ a could be 8
Step 2: 20=8×2+4 ⇒ HCF(20, 8) = HCF(8,4) ⇒ b could be 4
Step 3: 8=4×2+0
HCF = 4
Since 1008=20×q+a where q and a are positive integers satisfy Euclid’s Division Lemma, we must have 0≤a<20. So a is surely 8 and b is 4.