Sub-Terahertz (THz) frequencies between 100 GHz and 300 GHz are being considered as a key enabler for the sixth-generation (6G) wireless communications due to the vast amounts of unused spectrum. The 3rd Generation Partnership Project (3GPP) included the indoor industrial environments as a scenario of interest since Release 15. This paper presents recent sub-THz channel measurements using directional horn antennas of 27 dBi gain at 142 GHz in a factory building, which hosts equipment manufacturing startups. Directional measurements with co-polarized and cross-polarized antenna configurations were conducted over distances from 6 to 40 meters. Omnidirectional and directional path loss with two antenna polarization configurations produce the gross cross-polarization discrimination (XPD) with a mean of 27.7 dB, which suggests that dual-polarized antenna arrays can provide good multiplexing gain for sub-THz wireless systems. The measured power delay profile and power angular spectrum show the maximum root mean square (RMS) delay spread of 66.0 nanoseconds and the maximum RMS angular spread of 103.7 degrees using a 30 dB threshold, indicating the factory scenario is a rich-scattering environment due to a massive number of metal structures and objects. This work will facilitate emerging sub-THz applications such as super-resolution sensing and positioning for future smart factories.