Question

By Euclid algorithm find HCF of 65 and 117 and find the pair of integral values of m and n such that HCF = 65m + 117n

Answer 1

Answer: here is your answer

Step-by-step explanation:

By Euclid's division algorithm  

117 = 65 x 1 + 52.

65 = 52 x 1 + 13

52 = 13 x 4 + 0

Therefore 13 is the H.C.F (65, 117).

13 = 65 + 52 x(-1)

13 = 65 + [117 + 65 x(-1)]x(-1)

13 = 65 x(2) + 117 x(-1).

∴ m = 2 and n = -1.

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Answer 2

Answer: CRACYFORSTUDIES

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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