Is continuous inputs an assumption of factor analysis? Should we use only continuous inputs for factor analysis (FA)? My data is a mix of continuous and categorical inputs: one of the inputs has only 600, 700 and 1000 as values. 
I found that principal component analysis (PCA) isn't suitable for mixed data but didn't find any FA assumption of continuous inputs.
 A: Do not mix up concepts "categorical" (such as A, B, C or "low", "medium", "high") and "discrete metrical" (such as 600, 700, 1000). Any empirical dataset is more or less discrete observed values. If you agree and wish to acknowledge the fact that 1000 is thrice more distant from 700 than 700 is from 600 your scale is metrical aka scale aka quantitative, though it is not necessarily continuous by observation or by nature. Continuity underlies it metaphysically (as a potentiality to grain a gauge more finely, up to the interpolation between notches). [For term "quantitative" - it is a bit ambiguous because ordered categorical data also reflects quantity, in a sense.]
Linear factor analysis requires scale/metrical data (that is, all variables interval or all variables ratio level of measurement) because it assumes factors are continuous inderlying latent features (see alternative methods). So, you may take your 600, 700, 1000 variable in FA along with other ones, but you should base your analysis on correlations (or cosines) because of different measurement units involed.
Plain (linear) factor analysis should of course not be used with ordinal data and is often considered inappropriate to use with binary data (but it is not a sin to do PCA with binary data unless you consider the components as "latent factors").
Factor analysis should not be performed on Spearman or Kendall correlations.
