Wolfram Alpha:

Factor Analysis
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The key concept of factor analysis is that multiple observed
variables have similar patterns of responses because they are
all associated with a latent (i.e. not directly measured)
variable.

For example, people may respond similarly to questions about
income, education, and occupation, which are all associated
with the latent variable socioeconomic status.

When you find a set of variables that are highly correlated
with each other, it is reasonable to wonder if this mutual
association may be due to some common underlying cause.
The purpose of Factor Analysis is to identify a set of
underlying factors that explain the relationships between
correlated variables. Generally, there will be fewer
underlying factors than variables, so the factor analysis
result is simpler than the original set of variables.

One of the most useful ways to determine the number of
factors to use is by means of a SCREE PLOT that shows what
percentage of the variance is accounted for by each factor.

The horizontal axis shows the number of factors. The
vertical axis shows the percent of the overall variance
explained by each factor. A sharp drop off indicates the
number of factors that should be retained.