"Jedaiah," "Jehoiarib," and "Jachin," are not here names of individuals but of priestly families. From 1-Chronicles 24:7-17, it appears that Jehoiarib was the original head of the first "course," Jedaiah of the second shift, and Jachin of the twenty-first shift.

And of the priests,.... Who returned and dwelt at Jerusalem:
Jedaiah, and Jehoiarib, and Jachin; Jedaiah was the son of Jehoiarib, and Jachin is called Jachin, Nehemiah 11:10.

The priests. - The three names Jedaiah, Jehoiarib, and Jachin (1-Chronicles 9:10) denote three classes of priests (cf. 1-Chronicles 24:7, 1-Chronicles 24:17), who accordingly dwelt in Jerusalem. There also dwelt there (1-Chronicles 9:11) Azariah the son of Hilkiah, etc., the prince of the house of God; cf. 2-Chronicles 31:13. This is the Azariah mentioned in 1-Chronicles 6:13, the son of Hilkiah, etc., the grandfather of the Jehozadak who was led captive into Babylon. then in 1-Chronicles 9:12 we have two other heads of the priestly fathers'-houses, with an enumeration of their ancestors, through whom they are traced back to the classes of priests to which they belonged respectively, viz., Adaiah to the class Malchijah (1-Chronicles 24:9), and Maasiai to the class Immer (1-Chronicles 24:14). According to this, therefore, there dwelt at Jerusalem, of the priesthood, the three classes Jedaiah, Jehoiarib, and Jachin, Azariah the prince of the temple, and of the classes Malchijah and Immer, the fathers'-houses Adaiah and Maasiai. In 1-Chronicles 9:13 the whole number is estimated at 1760. A difficulty is raised by the first words of this verse, "And their brethren, heads of their fathers'-houses, 1760," which can hardly be taken in any other sense than as denoting that the number of the heads of the fathers'-houses amounted to 1760. This, however, is not conceivable, as "fathers'-houses" are not single households, but larger groups of related families. Moreover, אחיהם, which is co-ordinate with the heads of the fathers'-houses, can only denote, as in 1-Chronicles 9:6, 1-Chronicles 9:9, the heads of the families which belonged to or constituted the fathers'-houses. To arrive at this meaning, however, we must transpose the words ואחיהם and לבית־אבותם ראשׁים, connecting לבית־אבותם ר with 1-Chronicles 9:12, and אחיהם with the number, thus: heads of fathers'-houses, etc., were those mentioned in 1-Chronicles 9:12, and their brethren 1760 (men), valiant heroes in the work of the service of the house of God. Before מלאכת one would expect the word עשׁי, as in 1-Chronicles 23:24 and Nehemiah 11:12, but its presence is not so absolutely necessary as to warrant us in supposing that it has been dropped out, and in inserting it. מלאכת may be also taken as an accusative of relation, "valiant heroes in reference to the work;" or at most a ל a tso may be supplied before מלאכת, as it might easily have been omitted by a clerical error after the immediately preceding חיל. On comparing our passage with Nehemiah 11:10-14, we find there, if בּן־יויריב in 1-Chronicles 9:10 be altered into יהויריב, the same three classes of priests; but instead of Azariah, Seraiah is prince of the house of God, 1-Chronicles 9:11 : thereafter we have 822 brethren, performing the work of the house (of God). Then follows Adaiah of the class Malchijah (as in the Chronicles), but with the addition, "his brethren 242;" and then Amashai of the class Immer, but with other ancestors than those of the Maasiai of the Chronicles, and with the addition, "and their brethren, valiant heroes, 128;" and finally, Zabdiel Ben Hagdolim as overseer (president over them).
The sum of the three numbers is 1192, as contrasted with the 1760 of the Chronicle.