Three pure factors

The three pure factors, by means of which an arhat teaches, are:

Firstly there is the pure vessel of the listener (Tib. སྙན་པ་པོའི་སྣོད་དག་པ་, Wyl. snyan pa po'i snod dag pa). This means that the arhats use their supernatural powers of cognition to examine the students in the assembly before teaching the Dharma only to those whose mindstreams are pure.
Then there is the pure speech of the teacher (Tib. འཆད་པ་པོའི་ངག་དག་པ་, Wyl. chad pa po'i ngag dag pa). This means the arhats teach without any afflictive emotion, in a pleasant style that is free from any verbal impediment or any flaws in terms of grammar or syntax.
Finally there is the pure topic of the teaching (Tib. གསུང་རབ་ཀྱི་བརྗོད་བྱ་དག་པ་, Wyl. gsung rab kyi brjod bya dag pa) which means that the arhats teach exactly what they heard from their own teachers, the perfectly enlightened buddhas. They do not add or omit even so much as a single word on account of their infallible powers of recollection.

You might wonder why the great arhats do not teach the Dharma through the three types of miraculous ability. Arhats are unable to teach using these three miraculous abilities because they have four causes that prevent them from knowing certain things.^[1]

References

↑ *Patrul Rinpoche, Preliminary Points To be Explained when Teaching the Buddha's Word or the Treatises, translated by Adam Pearcey.