# Factor a Vector

Does there exist a function in Mathematica that simply takes out a common factor from a vector/list of expressions? This seems like such a simple operation that I am surprised that I could not find it in Google or the Mathematica help. It could return the common factor and the list without it:

Function[{a b c , b c, c d}] = {c,{a b, b, d}}


Or it could even simply return the common factor:

Function[{a b c , b c, c d}] = c


edit: sorry I was not completely clear. It would factor out algebraic expression too. So:

Function[{x^2 y, x}]


would yield:

{x,{x y, 1}}

• A "common factor", where all having it is a given? Intersection @@ list – ciao Mar 22 '14 at 0:49

test = {x^2 y, x};

p = PolynomialGCD @@ test
{p, test/p}

test = {a b c e, b c e, c d e, e c};

p = PolynomialGCD @@ test
{p, test/p}

(*

{x, {x y, 1}}
{c e, {a b, b, d, 1}}

*)

• Thank you! PolynomialGCD was that function! – user2686410 Mar 22 '14 at 1:01