Were there many people who came and followed the Buddha during his lifetime?
佛在世的时候，归依的人多吗？

Yes. On the way from Sārnāth to Magadha State after the Buddha's first sermon, many people were converted to follow his teachings. Among them were three brothers, Brahmins, by the name of Kassapa. They had been Zoroastrians, but were now converted and brought along with them more than one thousand of their followers to be converted to Buddhism. After the Buddha arrived in Rājagaha, the capital of Magadha, many more people were converted, including some who were to become prominent disciples, like Sāriputta, Mahāmoggallāna and Mahākassapa. Afterwards, when the Buddha returned to his native land, a number of his relatives: his younger half brother Nanda, his cousins Ānanda and Devadatta, his son Rāhula became monastic disciples. Among them, there was a barber named Upãli, who had served the royal family, and later became a famous master of Buddhist disciplines (Vinaya bhānaka). The Buddha's aunt Prajāpati also followed to become the first female monastic disciple of the Buddha. Besides, even more devotees were converted to the faith without renouncing the home life. Therefore, the Buddha's disciples consist of Bhikkhu (monks) and Bhikkhunī (nuns), who form the Buddhist monastic order; and Upāsaka and Upāsikā, who are the male and female lay followers; together they are known as the four groups of disciples.
是的，佛初转法轮后从鹿野苑到摩揭陀国（Magadha）去的一路上，受到他的教化而归依的人就很多。其中有拜火教的婆罗门姓迦叶的三兄弟，都改变了原来的信仰，率领他们的弟子一千多人归依了佛教。佛到了摩揭陀国首都王舍城（Rājagaha）后，归依的人更多。其中最有名的出家弟子有舍利弗（Sāriputta）、摩诃目犍连（Mahāmoggallāna）、摩诃迦叶（Mahākassapa）等人。后来佛回到故乡去，他的异母弟难陀（Nanda）、堂兄弟阿难陀（Ānanda）、提婆达多（Devadatta）和他儿子罗怙罗等都随他出了家。还有宫廷中一个剃发工奴优波离（Upāli）也出家加入了僧团，后来成为有名的佛教戒律学大师。佛的姨母波阇波提也归依了佛，是第一个出家女弟子。至于不出家而归依三宝的弟子则为数更多。佛的出家弟子，男的叫比丘（bhikkhu），女的叫做比丘尼（bhikkhunī）；在家弟子，男的叫做邬波索迦（upāsaka），女的叫做邬波斯迦（upāsikā），合称为四众弟子。