Question

If hcf of 1008, 20 is equals to 20, a is equals to hcf of 1008 is equal to 20 into q + a 20 = inr to m + b where q and a and m and b are positive integers satisfying euclid's division lemma what could be the values of a and b

Answer 1

Answer:

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 = 20x50+8 => HCF(1008, 20) = HCF(20, 8) => 'a' could be 8

• Step 2 : 20 = 8x2+4 => HCF(8, 4) => 'b' could be 4

• Step 3 : 8 = 4x2+0

→ HCF = 4

SINCE 1008 = 20Xq+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.