What is the evidence for the number of rak'ahs in each prayer?

Allah Almighty obligated five prayers upon His servants. Initially, the prayer consisted of two rak'ahs when resident and when traveling. Then, the number of rak'ahs for prayer while resident was increased, so Dhuhr, Asr, and Isha prayers became four rak'ahs, Fajr prayer remained two rak'ahs, and Maghrib prayer became three rak'ahs. It has been transmitted recurrently from the Prophet, peace and blessings be upon him, that he used to pray the five prayers with the currently known number, and scholars have unanimously agreed upon this number of rak'ahs for each prayer.