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Math Help - greatest common divisors

  1. #1
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    greatest common divisors

    if d = gcd(a, a_1 a_2...a_n) and d l gcd(d,a_1) gcd(d,a_2)...gcd(d,a_n) then why is it that d l gcd(a,a_1) gcd(a,a_2)...gcd(a,a_n)?
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  2. #2
    Junior Member
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    Mar 2012
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    Bogota D.D
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    Re: greatest common divisors

    Hi.

    Do you want to show that d|gcd(a,a_1)\cdot{gcd(a,a_2)}...\cdot{gcd(a,a_n)}?

    Best regards.
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  3. #3
    Super Member
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    Re: greatest common divisors

    yes. i know that d l a and dl a_1...a_n but how do i know that d l gcd( a, a_1) ...gcd(a, a_n)
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