I think it's not just about the sheer amount of papers one writes, but also the impact they have on the literature. And for Euler, he was lucky to live in an era without the problems of lengthy review processes as we see today.
"So prolific was he that the journal of the St. Petersburg Academy was still publishing the backlog of his papers a full 48 years after his death." – Euler: The Master Of Us All
p.s. Last year I read his Introductio in analysin infinitorum (1748), "one of the most influential mathematics books of all time", which made the function concept basic in mathematics. Polynomials, trig functions, exponential functions, the logarithm function, etc etc - doing amazing things with infinite series. It was hard to believe it wasn't a thoroughly modernised text, everything looks so modern, but it's just that he introduced a lot of our notation. And he explains things so helpfully and modestly. A joy to read, highly recommended.