Find HCF of 65 and 117 and find a pair of integral values of m and n.such that HCF=65m+117n.
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Answered by
405
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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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.
Here's Your Answer
Hope it Helps
Cheers , Have an amazing day :)
Answered by
55
Answer:
M=2,n=-1
By euclid's division lemma do and find the hcf of 117 and 65 and we will be able to get 13.and reverse the step 2like 65-52*1=13
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