Let P(m) denote the largest prime factor of an integer m ≥ 2, and put P(0) = P(1) = 1. For an integer k ≥ 2, let [Formula: see text] be the k-generalized Fibonacci sequence which starts with 0, …, 0, 1 (k terms) and each term afterwards is the sum of the k preceding terms. Here, we show that if n ≥ k+2, then [Formula: see text]. Furthermore, we determine all the k-Fibonacci numbers [Formula: see text] whose largest prime factor is less than or equal to 7.