When two people eat together, even though one may recite the beracha of hamotzi for the other, it is a mitzvah for each one to recite birkas hamazon for himself. This is true when both of them know how to recite birkas hamazon. If one knows and the other doesn’t the one who knows how should recite the beracha and the other will fulfill his obligation assuming he understands lashon kodesh but doesn’t know how to recite birkas hamazon. He must listen to each word that is recited....Rama: The one reciting the beracha must have in mind to discharge his friend’s obligation. Mechaber: If he does not understand he does not fulfill his obligation by listening. When three people eat together they may not separate and when two people eat together it is a mitzvah for them to search for a third to join their zimun. When four or five people eat together they may not separate since they are all obligated to make a zimuun. When the group is comprised of six they may separate since each group will make its own zimun and this is true until the group reaches ten. Once the group contains between ten and twenty people they may not separate until there are twenty since they will mention Hashem’s Name
Even if they were not initially established to eat together, but rather two people established a meal and afterward a third came and joined them, or one person established a meal at first and afterward the other two joined him — they are not permitted to separate, since they are considered fixed together at the end of the meal. However, in any case, if one eats with them without establishing (a meal) with them, they are permitted to separate — unless he is a servant. Rema : Nevertheless, even in any case where they are permitted to separate, it is preferable to make a zimun (invitation to bless) because “in a multitude of people is the King's glory” (Proverbs 14:28) (Beit Yosef).
If they were riding and said, “Let us eat,” even if each one eats from his own loaf and they did not dismount from their animals, they are joined (for zimun), since they stayed in one place. But if they were walking and eating — they are not joined. And if they were eating scattered and separated in a field, even if they are all eating at the same time and from the same loaf, since they did not designate a place to eat, they are not joined. Rema : The custom is not to perform a zimun in a non-Jew’s house, and the reason seems to be that they cannot establish themselves (for a meal) in a non-Jew’s house due to fear of the non-Jew, and it is as if they ate without establishing (a meal). Furthermore, there is concern for danger if they alter the wording of the blessing and do not say, “May the Merciful One bless this household.” Therefore, from the outset, they did not establish themselves, but rather each one intended to bless on his own. And thus the custom should not be changed, even if these reasons are not entirely sufficient — nevertheless, since the custom has already been established, it is as if they did not establish themselves together.
Three that sat down to eat and recited Hamotzi, even if they eat from their own loaf and they did not eat a kezayit, still they are forbidden to disband.
If three people come from three separate groups, each of which had three individuals, and these three (representatives) then joined together — if a zimun was already made in their original places (i.e., each group paused and two remained while the third led the zimun until saying “He Who provides…”), they can no longer perform a zimun together, even if they later eat together and finish their meal. But if no zimun was made in their original groups, they are obligated to make a zimun and are not permitted to separate — even if these three did not eat together after joining.
If there were three groups, each consisting of four people, and one person from each group left and joined together to form a new group, and the three who remained in each original group made a zimun — the zimun (obligation) is nullified for those who left, since their original groups already performed a zimun. The same applies if each original group had only three members, and one person from each group left before the zimun and the three who left joined together — and then someone joined each of the original two remaining in the groups to form three again and they made zimun — still, the zimun is nullified for the three who left, since their original groups already performed zimun, even though the zimun was made without them. Rema : If there were three groups, each with three people eating, it is forbidden for one person from each group to leave and join together for a zimun, since the two remaining in each group will no longer be able to make a zimun. But if each group had four people, then it is permitted for one person from each group to leave and join together for a zimun, and the remaining three in each group can make zimun in their original places (Beit Yosef in the name of the Rashba).