Dear Waqar Ahmed Sethar

The are multiple approaches to estimate the minimum sample size. However, the number of factor solely is not enough to answer this question.

These techniques differs in their complexity.

Relying on either:

1. Rule of thumb

2. Power Analysis

3. Monte Carlo Simulation

And I would recommend you to take a look into this paper that may give you the guidance to fulfill your sample size requirements sufficiently.

Here is the paper link:

https://www.researchgate.net/publication/327180990_Applied_Psychometrics_Sample_Size_and_Sample_Power_Considerations_in_Factor_Analysis_EFA_CFA_and_SEM_in_General

Here is the citation:

Kyriazos, T. (2018) Applied Psychometrics: Sample Size and Sample Power Considerations in Factor Analysis (EFA, CFA) and SEM in General. Psychology, 9, 2207-2230. doi: 10.4236/psych.2018.98126.

Waqar Ahmed Sethar, your question appears to be simple, but unfortunately the possible answers to it can be complex - particularly because satisfying some of the criteria associated with identifying an appropriate sample size can be determined only after you have actually obtained your data.

In your case, I would recommend aiming for at least 100 participants, at least in the first instance. In making this recommendation, I am relying on the good old rules of thumb as well as an assumption that the psychometric properties of your data (e.g., item communalities and loadings) will be sufficiently good for that number of participants.

If you need support for your decision, I think you could cite some of the texts that are referred to in the Kyriazos (2018) article that you've bee recommended in the post above here.

How many items?

There are 56 items

Waqar Ahmed Sethar, thank you for letting people know that you have 56 items. When you said you had 8 variables, I thought you were referring to items. Different people use different words for the same things.

In that case, I think you should aim for around 400 to 500 participants. Sorry for my misunderstanding.

Dear Robert Treventhan Thanks for sharing very precious information...it was