Calculate the fewest zip codes, for the largest coverage

[Larz60+]

One way to do this is to use the us Census Bureau GeoCoder.
The main site is here: https://geocoding.geo.census.gov/
You can submit an address batch file if you want to do it by street
addresses (if you don't know latitude and longtitude, which by the way
can be calculated if you know center lat and lon,  distance from center
and angle to point.

Given that information, you will receive:

Output:
Counties:
OID: 27590286621899
STATE: 33
FUNCSTAT: A
AREAWATER: 177190123
NAME: Belknap County
LSADC: 06
CENTLON: -071.4224504
BASENAME: Belknap
INTPTLAT: +43.5191091
COUNTYCC: H1
MTFCC: G4020
COUNTY: 001
GEOID: 33001
CENTLAT: +43.5179017
INTPTLON: -071.4253661
AREALAND: 1040130770
COUNTYNS: 00873174
OBJECTID: 3195

Here's a document that explains the whole process: https://www.census.gov/mso/www/training/...-13-16.pdf
And another for finding lat and long from bearing and distance from a point: http://www.movable-type.co.uk/scripts/latlong.html

You can also download all of the raw data (Tiger files) if you want to do it all yourself.
But a lot easier to use the api.