Question

By using euclid's algorithm find the HCF of 65 and 117 and find the pair of integral values of m and n such that HCF=65m+117n

Answer 1

By Euclid's division algorithm 

117 = 65x1 + 52.

65 = 52x1 + 13

52 = 13x4 + 0

Therefore 13 is the HCF (65, 117).

Now work backwards:

13 = 65 + 52x(-1)

13 = 65 + [117 + 65x(-1)]x(-1)

13 = 65x(2) + 117x(-1).

∴ m = 2 and n = -1.


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Answer 2

Answer:

m=2 and n = -1

Step-by-step explanation:

By Euclid’s division algorithm

117= 65x1+52

65= 52x1+13

52= 13x4+0

therefore 13bis the HCF (65,116)

13= +52×(-1)

13=65+[117+65×(-1)]×(-1)

13=65×(2)×117(-1)

answer : m=2 n=(-1)