Brachot 50 - How to invite to prayer
As we learned before , if at least three people ate together, they must call each other to join in the after-meal prayer. One should include himself in the call and say "Let us bless Him Whose food we have eaten," and if there are ten or more, he adds the name of God, saying, "Let us bless God..." If there are more than ten, he still calls them in the same way - these are the words of Rabbi Akiva, who compares this to a prayer leader in the synagogue: such leader does not turn back to count the number of people, and does not change his words based on the size of the group.
However, Rabbi Yose HaGlili bases his logic on the phrase, " Bless God in congregations, " which he understands to mean that the text of the call depends on the size of the congregation. For example, if more than ten thousand people ate together, one would say "Let us bless God our Lord, the God of Israel, Lord of Hosts, Who dwells by the Cherubim, for the food we have eaten."
Accordingly, if three people ate together, they are not allowed to separate and say their after-meal separately, for in doing so that would loose their common call to prayer, "zimun." The same is true for four and five, but six may separate into two groups of three. Again, ten people may not separate, but if there are twenty, they may form two groups of ten.
Art: Claude Oscar Monet - The Dinner