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Math Help - greatest common divisor

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    greatest common divisor

    if a and b are positive integers, show that gcd(a,b)=gcd(a,a+b),
    gcd represents the greatest common divisor.
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    Hello,
    Quote Originally Posted by tryitall34567 View Post
    if a and b are positive integers, show that gcd(a,b)=gcd(a,a+b),
    gcd represents the greatest common divisor.
    Let d=gcd(a,b)
    Let d'=gcd(a,a+b)

    d divides a and b. Hence it divides a+b too. So it divides both a & a+b. Then d divides d'.

    d' divides a and a+b. Hence it divides (a+b)-a=b. So it divides a & b. Then d' divides d.

    This shows that d=d'.
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