Let $𝒜$ be a commutative algebraic group defined over a number field $k$. We consider the following question:Let $r$ be a positive integer and let $P\in 𝒜\left(k\right)$. Suppose that for all but a finite number of primes $v$ of $k$, we have $P=r{D}_v$ for some $D_v\in 𝒜\left(k_v\right)$. Can one conclude that there exists $D\in 𝒜\left(k\right)$ such that $P=rD$?A complete answer for the case of the multiplicative group ${𝔾}_m$ is classical. We study other instances and in particular obtain an affirmative answer when $r$ is a prime and $𝒜$ is either an elliptic curve or a torus of small dimension...