According to what are the number of rak‘ahs and the manner of performing the prayers determined?

Acts of worship are tawqīfī. That is, it is not possible to fully comprehend the reasons for their obligation or their methods of performance solely through reason. Matters related to acts of worship are generally commanded in the Qur’an and have been clarified through the practice of the Prophet Muhammad (peace be upon him).

The Qur’an states that prayers are made obligatory at specific times (an-Nisā’, 4/103) and that they consist of certain pillars such as standing, recitation, bowing, and prostration. The details of this act of worship and other actions to be performed within the prayer have been established through the Sunnah of the Prophet (peace be upon him). (Bukhārī, Adhān, 95 [755-758]; Muslim, Salāt, 45 [397]; Masājid, 176 [613]) Expressing all this, the Prophet (peace be upon him) said, “Pray as you have seen me praying.” (Bukhārī, Adhān, 18 [631]) Accordingly, the general rulings, pillars, and conditions of prayer are determined by the Qur’an, while the details are specified by the Sunnah of the Messenger (peace be upon him).

Source: T.C. Diyanet İşleri Başkanlığı, Din İşleri Yüksek Kurulu