Well first, let's address the idea that Jesus lived for 33 (or to be more precise, 33 and a half) years. The belief that Jesus' public ministry lasted for three and a half years actually derives, not so much from the gospels, but from a Christological reading of the prophecy of Daniel's Seventy Weeks.
“Seventy weeks are decreed about your people and your holy city, to finish the transgression, to put an end to sin, and to atone for iniquity, to bring in everlasting righteousness, to seal both vision and prophet, and to anoint a most holy place. Know therefore and understand that from the going out of the word to restore and build Jerusalem to the coming of an anointed one, a prince, there shall be seven weeks. Then for sixty-two weeks it shall be built again with squares and moat, but in a troubled time. And after the sixty-two weeks, an anointed one shall be cut off and shall have nothing. And the people of the prince who is to come shall destroy the city and the sanctuary. Its end shall come with a flood, and to the end there shall be war. Desolations are decreed. And he shall make a strong covenant with many for one week, and for half of the week he shall put an end to sacrifice and offering. And on the wing of abominations shall come one who makes desolate, until the decreed end is poured out on the desolator.”
A common Christian interpretation of the passage is that the "he" who will make the sacrifices stop is the Antichrist (you may have heard this), but another interpretation applies it to Jesus.
The first recorded writer we have which drew the connection is Origen, who spoke of "about three years of the Lord's preaching," which he related to the half week in the prophecy of Daniel, but it was with Eusebius that the view became more or less the standard interpretation. In his Church History (1.10.2), for instance, he argues that: "The Divine Scripture says, moreover, that he passed the entire time of his ministry under the high priests Annas and Caiaphas, showing that in the time which belonged to the priesthood of those two men the whole period of his teaching was completed. Since he began his work during the high priesthood of Annas and taught until Caiaphas held the office, the entire time does not comprise quite four years." (This is often considered to be inaccurate nowadays, as Annas is generally held to have reigned from AD 6 to AD 15, which is way too early, and was first succeded by his son Eleazar before Caiaphas held the office in AD 18).
In his Demonstratio Evangelica (8.106-8) he cites the repeated Passovers in John's gospel as support of his view: "the whole period of our Savior's teaching and marvel-working is recorded to have been three years and a half, which is half of a week. This, I take it, John the Evangelist accurately establishes by his presentation in the gospel." We must note that Eusebius claimed that John represents a three-year ministry, but offered no specific arguments as proof. He notably did not use the argument that some supporters now use that the unnamed feast of John 5:1 as a fourth Passover.
Finally, in his Prophetic Eclogues (3.46) he supplements the exegetical point with a typological one, by drawing out a connection between Daniel's prophecy and Jesus' ministry: "Therefore it is written, 'and in the midst of the week shall be taken away sacrifice and libation'; (Daniel 9:27) and it is clear that with the Passion was forcibly taken from them sacrifice and libation, when according to the Evangelical Scripture 'the veil of the Temple was rent from the top to the bottom' (Matthew 27:41).
Eusebius' view proved to be convincing enough that later chroniclers and scholars came to adopt his view, first in the East, and then by the 6th century also in the West. I should note that up to this point, there seem to have been no agreement on the exact duration of Jesus' public ministry: Julius Africanus, Clement of Alexandria, and even some gnostic groups are said to have reckoned it to last a single year, St. Epiphanius contra Clement thought it lasted two years, and so on and so forth.