All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
The scholars did not determine precisely the number of Saheeh [sound] Ahaadeeth of the Prophet and we have not come across such a statement of them in this regard. Indeed, it is difficult to determine a specific number of it because classifying the Hadeeth as Saheeh and Dha’eef [weak] is a relative matter, as a Hadeeth may be classified as Saheeh by some scholars and weak according to some others. For more benefit, please refer to Fatwa 106653.
Besides, the Mutawaatir Hadeeth (i.e. the Hadeeth that was transmitted through a chain of narrators, each stage of which included a large number of narrators whose collusive fabrication of the Hadeeth is imperceptible) is included in the Saheeh Ahaadeeth.
The soundest Ahaadeeth are those reported by Al-Bukhari and Muslim and the entire Muslim nation have accepted them as authentic as An-Nawawi said. For more benefit, please refer to Fatwa 83766.
Also, it is difficult to determine the number of the Mutawaatir Ahaadeeth and this is due to the difference of opinion among the scholars in regard to the Mutawaatir Hadeeth. It might be that a scholar says that a given Hadeeth is Mutawaatir and another scholar says that it is not so.
Shaykh Muhammad Ibn Ja’far Al-Kittaani in his book ‘Nathm al-Mutanaathir min al-Hadeeth al-Mutawaatir’ quoted As-Sindi as saying in his commentary on “An-Nukhbah”: “As-Sayooti was very lenient in classifying the Mutawaatir Ahaadeeth, and he classified many Ahaadeeth as such and mentioned them in his book which he entitled ‘Al-Azhaar al-Mutanaathirah fil Ahaadeeth al-Mutawaatirah’ then Al-Kittaani said commenting on this: “Yes, it is truly so, as he mentioned (in his book) some Ahaadeeth which the scholars of Hadeeth authoritatively asserted that they are not Mutawaatir. Moreover, it appears from his statement that he intended to gather the Ahaadeeth that are Mutawaatir in their wording, but so many times he mentioned some Ahaadeeth which he or other scholars clarified in some books that they are Mutawaatir in their subject or meaning.”
Finally, it should be noted that just knowing the number of the Saheeh or Mutawaatir Ahaadeeth does not lead to any ruling or action, so not knowing it does not harm at all. Rather, a Muslim should be concerned about acting upon the Saheeh Ahaadeeth that reached him, and he should be keen on memorizing them and conveying them to other people.
Allaah Knows best.