In this paper, we will study some properties of the extended Eulerian numbers ${H}$(${n}$,${λ}$) with a parameter ${λ}$. In fact, for any integer ${n}$ we investigate the asymptotic behavior, find lower and upper bounds for ${H}$(${n}$). As application, for a champion number ${N}$, we obtain asymptotic formulas, lower and upper bounds of the arithmetic functions ꞷ(${N}$) and Ω(${N}$).