I think this answer from the Judaism site sums it up:
7 is the length of time for a natural cycle to transpire, often ending
with holiness/sanctification of some sort (the pattern set by
7 is special because it was set down by God as the natural cycle in creation.
In the same question above is this answer about other numbers:
It mentions the numbers:
1, (2?), 4, (5?), (6?), 7, 8, 10, 12, 40, and 70 all have
See that answer for full details of their importance.
Also important is the number 50 for Jubilee (from this answer):
Toward the end of the book of Leviticus the 7 day measure that is most
familiarly the Sabbath is unrolled across years to be the sabbatical
year, and across decades to be the Jubilee. The Jubilee is the 50th
year - the crown of the 7th 7.