Houston is entirely inside Harris County
Every one of the 178 ZIP codes USPS lists with Houston as the primary place name sits inside Harris County, Texas -- no cross-county split the way some major US cities have. Harris County was founded on December 22, 1836, and organized the following March; Houston was named the county seat that same December, and has held the role ever since. The county takes its name from John Richardson Harris, who founded the town of Harrisburg on Buffalo Bayou a decade earlier, in 1826.
Harris County is about to become the second-largest county in the US
Harris County's population of roughly 5.01 million currently ranks third nationally, behind Los Angeles County, California and Cook County, Illinois (Chicago). But Harris County added about 106,000 residents in a single recent 12-month period -- more than any other county in the country -- while Cook County lost population over the same stretch. On current trends, Harris is projected to pass Cook and become the second-most-populous county in the US, a shift that would end Cook County's decades-long hold on that spot.