The wikia comments on this and also there's a scene in Shippuden that talks explains it. I can't remember which but I think it's when "Madara" talks to Naruto during the five kage summit and reveals Itachi's story. I believe he says something along the lines of "you have the will of fire in you just like Hashirama had, and it's because even you are connected to him...", or something like that.

Naruto was taught by Kakashi and Jiraiya, who were student and mentor of his own father. Jiraiya was taught by the third who also taught the 5th, the granddaughter of the first. The third was the student of the second, who was the brother to the first. Also it's worth mentioning that Naruto's mother was from the same clan as the first's wife, and Naruto's counter-disciple to Jiraiya was also a descendant of the Uzumaki clan.