Answer :

When determining which refrigerant new household refrigerators should not be factory charged with, it's important to consider various factors, including the refrigerant's properties, environmental impact, and compatibility with typical refrigeration systems used in households.

Step-by-Step Analysis:

1. R-290 (Propane):
- R-290, also known as propane, is a hydrocarbon refrigerant. It has a relatively low Global Warming Potential (GWP) and is popular for its high efficiency and low environmental impact.
- However, because R-290 is flammable, it must be handled with caution, and its use might be restricted in certain applications.

2. R-450-A:
- R-450-A is a mixture of different refrigerants. It is also designed to have a low GWP and is used in various refrigeration applications. It is considered safer and less harmful to the environment compared to traditional high-GWP refrigerants.

3. R-600-a (Isobutane):
- R-600-a, or isobutane, is another hydrocarbon refrigerant. It is widely used in household refrigerators because of its high efficiency and low GWP. Similar to R-290, it is also flammable but has been widely adopted due to its environmental benefits.

4. R-404A:
- R-404A is a blend of refrigerants commonly used in commercial refrigeration solutions. It has been widely used in the past but has a very high GWP compared to the other refrigerants listed.
- Due to its high GWP and the environmental damage associated with it, its use is being phased out in many places in favor of more environmentally friendly options.

Given the choices, the correct answer is:

R-404A

Household refrigerators should not be factory charged with R-404A due to its high Global Warming Potential and environmental impact. The other refrigerants listed (R-290, R-450-A, and R-600-a) are either low-GWP options or have better environmental profiles suited for household applications.