There is no scientific answer to this question, and methodologists differ. Alternative arbitrary "rules of thumb," in descending order of popularity, include those below. These are not mutually exclusive: Bryant and Yarnold, for instance, endorse both STV and the Rule of 200. There is near universal agreement that factor analysis is inappropriate when sample size is below 50.
1. Rule of 10. There should be at least 10 cases for each item in the instrument being used.
2. STV ratio. The subjects-to-variables ratio should be no lower than 5 (Bryant and Yarnold, 1995)
3. Rule of 100: The number of subjects should be the larger of 5 times the number of variables, or 100. Even more subjects are needed when communalities are low and/or few variables load on each factor. (Hatcher, 1994)
4. Rule of 150: Hutcheson and Sofroniou (1999) recommends at least 150 - 300 cases, more toward the 150 end when there are a few highly correlated variables, as would be the case when collapsing highly multicollinear variables.
5. Rule of 200. There should be at least 200 cases, regardless of STV (Gorsuch, 1983)
6. Rule of 300. There should be at least 300 cases (Norušis, 2005: 400).
7. Significance rule. There should be 51 more cases than the number of variables, to support chi-square testing (Lawley and Maxwell, 1971)

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