generally, if you apply exploratory factor analysis, the analysis is based on the correlation matrix, so variables are standardized anyway. In a CFA (which you should apply if you have a presumption about which items measure which factors), the analysis is based on the covariance matrix. Normally, this should work but sometimes the algorithm has problems to converge.
With regard to your 4 point scale, however, I doubt that this scale deviates strongly from assumptions about the variables. I would use the DWLS estimator in R's lavaan to consider this.
Nirosha Edirisinghe First of all you should look at your sample size. The main differences between components analysis and factor analysis (if you like to know) is that the two procedures are equivalent in practice if the data are well structured, however be very cautious of its validity when the measured variables (items) have low communality and the factors (or components) have few salient loadings, then components analysis and factor analysis results can differ markedly.
If you run factor analysis in the correlation matrix and not the covariance matrix is the same as standardizing the variables, and then factoring the covariance matrix. Therefore, no need to standardize variables before you run the factor analysis.