You need at least 300 participants to generate reliable results. More than 300 is the best. 

Dear Rajeev,

According to Guadagnoli and Velicer (1988), the adequate sample size is related to the minimum component size on their main factor.

They advise applied researchers as follows:

The researcher, prior to an analysis, should select variables that will be good markers for a component--that is, variables that clearly should define a particular component and will load highly. If an a priori estimate of saturation level is difficult, many variables (10 or more) thought to represent a particular construct (component) should be selected. If these conditions can be accurately stipulated by the researcher beforehand, a sample size of 150 observations should be sufficient to obtain an accurate solution.

Following an analysis, the component pattern itself can be assessed with respect to the number of variables defining a component and with respect to the magnitude of component loadings. If components possess four or more variables with loadings above .60, the pattern may be interpreted whatever the sample size used. Similarly, a pattern composed of many variables per component (10 to 12) but low loadings (0.40) should be an accurate solution at all but the lowest sample sizes (N < 150). If a solution possesses components with only a few variables per component and low component loadings, the pattern should not be interpreted unless a sample size of 300 or more observations has been used. Replication is strongly suggested if these conditions occur when the sample size is fewer than 300 observations.

Although their paper states that any sample size is ok with high loadings there is a figure in the paper which suggests a sample size of 50 is ok for 4 loadings > 0.8 and a sample size of 100 is ok for 4 loadings > 0.6.

Reference:

Guadagnoli, E. and Velicer, W. F. (1988) Relation to sample size to the stability of component patterns. Psychological Bulletin, 103(2), pp. 265-275.

Respected sir

In the field of social science we considered factor loading was > 0.40 for >100 sample or and also check KMO test with the help of spss.

For the Factor Analysis method, researchers determine sample sizes in two ways. One method is to determine the minimum number of samples needed (N). Another method is to determine the sample size as a function of the number of variables. Also known as the subjects-to-variable ratio, (N:p) (Beavers et al., 2013; Guadagnoli & Velicer 1988; Hogarty et al., 2005). There are advantages, and disadvantages, of both methods. For most factor analysis studies, using a formula to determine sample size is most appropriate. Hogarty et al. (2005) found that a higher number of samples were necessary when the goal of the study goal was to understand which factors underlie which variables. When the study goal was to ensure that sample loadings correlated highly with population loadings, fewer samples were necessary (Hogarty et al., 2005). Comrey and Lee (1992) recommend a minimum of 5 observations per variable, or ideally 20 observations per variable.

Assume you have asurvey with 23 questions (23 variables). At a minimum 23*5 = 115 observations will be needed to perform a a factor analysis adequately. Ideally, 23*20 = 460 observations will be needed to perform a factor analysis. Assuming a 10% rate for invalid surveys and an average industry response rate of 20%, then a minimum of (115*1.10)/0.20 = 632 surveys must be administered.

REFERENCES

Beavers, A. S., Lounsbury, J. W., Richards, J. K., Huck, S. W., Skolits, G J., & Esquivel, S. L. (2013). Practical considerations for using exploratory factor analysis in educational research. Practical Assessment, Research & Evaluation, 18(6), 1-13. Retrieved from http://www.pareonline.net/pdf/v18n6.pdf

Comrey, A. L., & Lee, H. B. (1992). Interpretation and application of factor analytic results. Comrey AL, Lee HB. A first course in factor analysis, 2.

Guadagnoli, E. & Velicer, W. F. (1988). Relation of sample size to the stability of component patterns. Psychological Bulletin, 103, 265-275. doi:10.1037/0033-2909.103.2.265

Hogarty, K Y., Hines, C. V., Kromrey, J. D., Ferron, J. M., & Mumford, K. R. (2005). The quality of factor solutions in exploratory factor analysis: The influence of sample size, communality, and overdetermination. Educational and Psychological Measurement, 65, 202-226. doi:10.1177/0013164404267287

use the Kaiser-Meyer-Olkin (KMO) measure - in SPSS go to analyze/dimension reduction/factor/descriptives/KMO

you nedd a value higher than .60 (ideally .70)

You question needs to be understood at two different levles. An adequate response to the sample size dimension of your question your question was given in the paragraph writen by Linda Sanner which I copy and paste next.

Assume you have asurvey with 23 questions (23 variables). At a minimum 23*5 = 115 observations will be needed to perform a a factor analysis adequately. Ideally, 23*20 = 460 observations will be needed to perform a factor analysis. Assuming a 10% rate for invalid surveys and an average industry response rate of 20%, then a minimum of (115*1.10)/0.20 = 632 surveys must be administered. (Linda Sanner)

For the second aspect of your question, please folow the recommendation of Lisete Mónico 

Good luck

:

KMO and Bartlett's test can be used to evaluate if the obtained correlation matrix is suitable for factor analysis. To my knowledge, these tests are featured in every FA program (e.g., SPSS, R). Having an a priori level of N is not enough, you have to next determine if the obtained data are useful for analyses using the common factor model. 

Dear RG colleague,

The KMO statistic, which can vary from 0 to 1, indicates the degree to which each variable in a set is predicted without error by the other variables. A value of 0 indicates that the sum of partial correlations is large relative to the sum correlations, indicating factor analysis is likely to be inappropriate . A KMO value close to 1 indicates that the sum of partial correlations is not large relative to the sum of correlations and so factor analysis should yield distinct and reliable factors. Hair et al. (2006) suggest accepting a value of 0.5 or more. values between 0.5 and 0.7 are mediocre, and values between 0.7 and 0.8 are good.

Bartlett’s test of sphericity is a statistical test for the presence of correlations among variables, providing the statistical probability that the correlation matrix has significant correlations among at least some of variables. For factor analysis to work some relationships between variables are needed. Thus, a significant Bartlett’s test of sphericity is required, say p

Sincere thanks, I got my answer.

Regards

Thanks