What is the age of a Remington 760 with serial number 352868?

The model 760 "Gamemaster" with this serial number would have been manufactured between 1951 and 1967.

Here is a breakdown of serial number blocks for that model:

1951-1967: 1,000-541,000
1968-1975: 6,900,000-7,499,999
1975-1978: A6,900,000-A7,499,999
1978-1981: B6,900,000-B7,499,999