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    Number Systems

    If HCF (65,117) is expressed in the form 65m+117n, then find the value of m.
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    Quote Originally Posted by suthayil View Post
    If HCF (65,117) is expressed in the form 65m+117n, then find the value of m.
    You need to apply the Euclidean Algorithm:

    117 = 65x1 + 52.

    65 = 52x1 + 13

    52 = 13x4 + 0

    Therefore 13 is the HCF (65, 117).

    Now work backwards:

    13 = 65 + 52x(-1)

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

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

    Therefore m = 2 and n = -1.

    You should note however that m and n are NOT unique ....
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