Content and primitive integer polynomials

Let $0\ne f\in\mathbb Z[x]$. Through the trimmed-list correspondence (Finitely supported coefficient sequences and trimmed finite coefficient lists define the same formal polynomials), write $f=a_0+a_1x+\cdots+a_nx^n$ with $a_n\ne0$. Its content is the iterated nonnegative integer gcd

$\operatorname{cont}(f):=\gcd(\cdots\gcd(\gcd(0,a_0),a_1)\cdots,a_n),$

using the integer gcd of Common divisor, and the greatest common divisor $\gcd(a,b)$, with the convention $\gcd(0,0) := 0$. The result is positive because not every coefficient is zero. The polynomial $f$ is primitive when $\operatorname{cont}(f)=1$. Set $\operatorname{cont}(0):=0$, but do not call the zero polynomial primitive.

The value does not depend on appending trailing zero coefficients, and Content is the positive common divisor of the coefficients divisible by every common divisor ↗ proves its universal common-divisor characterization.