# Math Help - relatively prime problem

1. ## relatively prime problem

Hi,

Need help with this problem;

Let a,b1,b2,....bn E Z, with (a,b1)=(a,b2)=(a,b3)=....=(a,bn)=1

Prove that

(a,b1b2....bn) = 1

Thanks

2. ## Prime factors

Hello htata123
Originally Posted by htata123
Hi,

Need help with this problem;

Let a,b1,b2,....bn E Z, with (a,b1)=(a,b2)=(a,b3)=....=(a,bn)=1

Prove that

(a,b1b2....bn) = 1

Thanks
You need to consider the (unique) prime factorisation of $a$ and all the $b_i$, and then use the fact that $a$ does not have any prime factor in common with any of the $b_i$, and therefore neither with $\prod{b_i}$.