Question

Express HCF of 305 and 793 as 305x + 793y where x and y are integers.

Answer 1

Hi friend,

Here is your answer,

Euclid division lemma :-
a=bq+r

793=305(2)+183
305=183(1)+122
183=122(1)+61
122=61(2)+0
As the remainder is 0,hcf of 793 and 305 is 61.

61=183-122×1
61=183-[305-183×1]×1
61=183-305+183×1
61=183×2-305×1
61=[793-305×2]×2-305
61=793×2-305×4-305
61=793×2-305×5
61=-305×5+793×2
61=305(-5)+793(2)
61=305x+793y
where x=-5 and y=2

Hope it helps....☺