Question

find the HCF of 65 and 117 and express it in the form 65m +117n​

Answer 1

Answer: m=2 n=(-1)

Step-by-step explanation:

( step 1- find the HCF using Euclid's division lemma)

117=65*1+52------------(1)

65=52*1+13---------(2)

52=13*4+0

thus, HCF(117,65)=13

according to the problem,

HCF = 65m+117n

13=65m+117n

( from (2))-

13=65-52

13=65-(117-65) ( since 52=117-65 from (1)

13=65-117+65

13=2(65)-117

thus, m=2 and n=(-1)