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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- Apr 17th 2012, 06:14 PMalexandrabel90greatest 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)?

- Apr 18th 2012, 07:59 AMFernandoRe: greatest common divisors
Hi.

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

Best regards. - Apr 18th 2012, 08:19 AMalexandrabel90Re: 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)