Do only certain popes become saints?

Or, do all or most of them become saints? Some folks are acting like the beatification instantly popped up to be a distraction or good publicity for the Catholic Church. Although I don't think all or most popes become saints, I'm sure this was in the works for a long time. How many popes become saints? I'm Presbyterian, but am trying to learn more about Catholicism - that is where I've gone to church in recent years (Part of my family is Catholic.).