Here’s two patterns with the ages that lead me to think the point of the numbers was more symbolic than literal.
First, the ages of the main patriarchs.[1]
The factors of these ages include a square of 5, 6, 7. Then we get Joseph.
The factor apart from the square also has a pattern. For Joseph, it is simply 1 (the squares themselves), then 3 for Jacob, 5 for Isaac, 7 for Abraham. So it builds up to a 7 using odd numbers.
Seeing as these ages are all from the same book, this is hard to write off as coincidence. Since 110 was viewed as an ideal lifespan in Egypt, that was probably the starting point. Since that number contains the three squares, that may have led the author to the right meaningful numbers for the other patriarchs. But who knows.
The other pattern is even weirder. Adding the ages of all the patriarchs from Adam to Moses results in 12,600 years.[2] In days, 12,600 is exactly 35 years in the 360-day calendar often used in biblical times (or 7 x 5 years). Knock off a zero, and 1,260 days is exactly 3.5 years. This span of time is quite significant in Daniel (the “time, two times and half a time” of Dan. 7:25) and Revelation (11:2-3). There’s much more about this pattern here:
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I came across this in Victor P. Hamilton’s Book of Genesis 18-50 (NICOT), p. 709.
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Jeremy Northcote, “The Lifespans of the Patriarchs: Schematic Orderings in the Chrono-Genealogy”, Vetus Testamentum, 57(2), 2007, pp. 243-257.