A factor is, per OED:
An agent who buys and sells, or transacts other business, on behalf of another person or company, usually one based in a different place, on commission; a mercantile agent; a commission agent.
The term was once commonly used to define trading managers working for the East India Trading Company.
This meaning is in rare use today compared to other meanings of the word "factor," but it seems to carry a business-sense meaning that persists, and might be part of the reason it is found in so many business names, particularly British.
A factor is a financial intermediary that purchases receivables from a company. A factor is essentially a funding source that agrees to pay the company the value of the invoice less a discount for commission and fees. The factor advances most of the invoiced amount to the company immediately and the balance upon receipt of funds from the invoiced party.
It's also possible that the decision by these companies to use the word was influenced by OED definition II, which is in more common use today:
An element or constituent, esp. one which contributes to or influences a process or result.
An element which enters into the composition of something; a circumstance, fact, or influence which contributes to a result.
These definitions carry with them a sense of importance and significance, which lends itself as a useful term in marketing and branding. Furthermore, the terms carry a flavor of math and technology, which might be appealing to a company seeking to brand itself. Ultimately, why each company chose to use the word in their business name can only be subject to speculation.