Genesis names three sons of Noah before the Flood: Shem, Ham, and Japheth. Genesis 6:10 identifies the three sons as members of Noah’s household, and later chapters continue using their names in the post-Flood genealogy.
The three sons enter the Ark with Noah, Noah’s wife, and their own wives. Genesis 7:13 lists this family group among those preserved from the Flood. The narrative later presents the sons as ancestors of nations, with Genesis 10 traditionally called the Table of Nations.
Shem is especially important in the biblical genealogy leading toward Abraham, but that later connection does not change the number of sons named in the Flood account. Ham and Japheth are also explicitly named, so the complete answer is three.
Some retellings add unnamed children or focus only on one son because of later genealogical traditions. The Genesis text itself gives the concise family list of Shem, Ham, and Japheth.