# greatest common divisors

• April 17th 2012, 06:14 PM
alexandrabel90
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)?
• April 18th 2012, 07:59 AM
Fernando
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.
• April 18th 2012, 08:19 AM
alexandrabel90
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)