Question

Find the HCF of 65 and 117 and express it in the form of 65m + 117n.

Answer 1

Hey friend!!

Here's ur answer...

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$117 = 65 \times 1 + 52 \\ 65 = 52 \times 1 + 13 \\ 52 = 13 \times 4 + 0 \\ \\ so \: hcf \: = 13 \\ \\ \\ linear \: combination \: = \\ \\ 13 = 65 - (52 \times 1) \\ 13 = 65 - (117 - 65 \times 1) \\ 13 = 65 - 117 + 65 \\ 13 = 65 \times 2 - 117 \times 1 \\ 13 = 65 \times 2 + 117 \times - 1 \\ 13 = 65m + 117n \\ where \: m \: = 2 \: and \: n = - 1$


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Hope it may help you...


Thank you :) :))

Answer 2

117=65×1+52
65=52×1+13
52=13×4+0
hence 13 is hcf
so
13=65-52×1
13=65-(117-65×1)×1
13=65-117+65×1
13=65×2-117×1
13=65×2+117×-1
so,m=2,n=-1