Question

eclipse algorithm to find HCF of 117 and 65 and the express it in the form of 117 M + 65 n where M and n are integers

Answer 1

hello !!
117>65
applying Euclid's division lemma

117=65×1+52

applying division lemma again to 65 and 52

65=52×1+13

applying division lemma again to 52 and 13

52=13×4+0

HCF(117,65)=13

NOW ,
13=65-52×1
13=65-(117-65×1)×1
13=65+65-117
13=65(1+1)+117(-1)
13=65(2)+117(-1l
13=65n+117m
where n=2 and m= -1
hope this was helpful :)