There are a few different ways of reading and hearing this passage. One is to realize that Peter is asking Jesus if the rabbinic teaching of the day—you forgive someone three times but no more—is what Jesus agrees with. Peter seems to be showing great magnanimity.
Another is to recognize that even in that simpler time, there were people who got under the skin of others, and Peter was asking a question “for a friend,” functionally admitting that he was struggling with this question himself.
One way I have often listened to this little story is by remembering that Peter’s brother, Andrew, is one of the disciples as well. And yes, while blood is thicker than water, family knows how to push your buttons. I can imagine Andrew doing something to Peter that sends him over the edge, gets on his last nerve, goes “about as far as he can go” (with apologies to Rogers and Hammerstein in Oklahoma). Peter has had it. He is ready to help Andrew realize eschatology and go to the place from which Jesus brought Lazarus back.
“How many times, Jesus? Seven?”
There are some textual differences in the Greek text of Jesus’s answer. While most indicate that Jesus says seventy-seven, some say that Jesus replied, “seventy times seven.” (Even I know that’s 490.)
I imagine Peter’s jaw dropping. He now not only has to use his fingers AND his toes to count, he needs to carry around a clay tablet to keep count! But that’s not the point. Jesus is teaching by hyperbole. He is pointing out that as WE have been forgiven by God—so many times—so we are to become people who practice forgiveness. Without keeping count.
We forgive because we have been forgiven.