The Lie algebra of the conformal group is spanned by rotations, translations, dilations and transversions. For this reason, some physicists have believed that every element in the identity component of the conformal group could be expressed as a product of four factors including exactly one rotation, one translation, one dilation and one transversion. However, this does not hold, as shown by the counter-example of J. Maks in 1989. It seems that some physicists are still confused about the factorization of conformal transformations. This article points out errors in the recent literature on this topic and gives explicit counter-examples to misplaced claims.