The number was not firmly established in 1929, when Alexander Klemin wrote "Airplane Stress Analysis". The book has a section on "Department of Commerce Requirements", which explains a variety of terminology and factors that would be confusing if I didn't quote the entire chapter.
Although he comes at the numbers from empirical sources at the US Army and Navy, the factors he ends up using aren't too different from what we use today (Nman=3.98 instead of 3.8). Some are related to power loading, which is also interesting. Again, different terminology is used, but he does mention the "factor of safety". He used a factor of 2. That is:
"The load factor times the basic load is, then, the 'design load' or twice the maximum probably load that the plane is required to withstand."
Which is as close as he gets to saying that you multiply the limit load by the factor of safety for ultimate load.
Aeronautics Bulletin 7 was published by the Dept. of Commerce in 1934. It states:
"The minimum factor of safety for any aircraft structure or component thereof shall be 1.50 unless
otherwise specified."
And it's been that way ever since.
Why do you ask (If I may ask).
Steven Fahey, CET