Praise be to Allah.

Firstly: 

Al-Bukhaari (841) and Muslim (583) narrated from Ibn ‘Abbaas (may Allah be pleased with him) that raising the voice in dhikr after the people have finished the obligatory prayer is prescribed and was done at the time of the Prophet (blessings and peace of Allah be upon him). Ibn ‘Abbaas said: I would know when they had finished when I heard that. 

According to a report narrated by al-Bukhaari (842): I used to know when the prayer of the Prophet (blessings and peace of Allah be upon him) had ended from the takbeer. 

The scholars differed as to whether the dhikr and takbeer should be recited out loud after the prayer. 

The majority of fuqaha’ are of the view that it is not mustahabb to raise the voice in reciting the takbeer and dhikr after finishing the prayer. Ash-Shaafa‘i interpreted the hadiths which refer to the Prophet (blessings and peace of Allah be upon him) raising his voice in dhikr as meaning that the Prophet (blessings and peace of Allah be upon him) said these words out loud in order to teach the Sahaabah the words of dhikr, and that he did not do that all the time. 

Al-Mawsoo‘ah al-Fiqhiyyah (13/213) 

Some are of the view that it is mustahabb to raise the voice in dhikr following the prayer, including at-Tabari, Ibn Hazm, Shaykh al-Islam Ibn Taymiyah, and others. 

This matter is broad in scope, in sha Allah, and the difference of opinion concerning it is reasonable. The one who favours the view that one may raise the voice in dhikr following the prayer should do so in a moderate manner, without disturbing or annoying others. 

Please see the answer to question no. 87768 

Secondly: 

The scholars differed as to what is meant by takbeer as mentioned in the hadith of Ibn ‘Abbaas (may Allah be pleased with him). It was said that one should say takbeer three times after finishing the prayer. Ibn Rajab (may Allah have mercy on him) said: Imam Ahmad narrated that ‘Amr ibn Dinar said: When the imam said the salaam at the end of the prescribed prayer, the people used to say takbeer three times. 

Hanbal said: I heard Abu ‘Abdullah say: ‘Ali ibn Thaabit told us: Waasil told us: I saw ‘Ali ibn ‘Abdullah ibn ‘Abbaas, when he prayed, say takbeer three times. I said to Ahmad: After he finished praying? He said: Yes. I said to him: The hadith of ‘Amr, from Abu Ma‘bad, from Ibn ‘Abbaas (says): We used to know that the prayer of the Messenger of Allah (blessings and peace of Allah be upon him) had ended from the takbeer. Are these people following that? He said: Yes. Ibn Rajab said:

From this it is clear that what is meant by the takbeer as known at the time of the Messenger of Allah (blessings and peace of Allah be upon him) following the prescribed prayer was three consecutive takbeers. End quote. 

Fath al-Baari by Ibn Rajab (7/396) 

It was also suggested that what is meant by the takbeer is saying “Subhaan Allah, al-hamdu Lillah and Allahu akbar (Glory be to Allah, praise be to Allah, and Allah is Most Great)” thirty-three times following the prayer. 

The scholars of the Standing Committee were asked: 

Is it prescribed for the worshipper to say after the tasleem, “Allahu akbar” before praying for forgiveness three times, based on the word takbeer in the hadith of Ibn ‘Abbaas (may Allah be pleased with him), in which he said: I used to know that the prayer of the Messenger of Allah (blessings and peace of Allah be upon him) had ended from the takbeer (agreed upon)? If that is not permissible, then what is meant by takbeer in this hadith? 

They replied: 

When the Prophet (blessings and peace of Allah be upon him) said the tasleem at the end of the prayer, he would start by asking Allah for forgiveness three times, then he would say “Allaahumma anta al-salaam wa minka al-salaam, tabaarakta yaa dhaa’l-jalaali wa’l-ikraam (O Allaah, You are al-Salaam (the One Who is free from all defects and deficiencies) and from You is all peace, blessed are You, Possessor of majesty and honour)”. Then he would recite the rest of the adhkaar that have been narrated. As for the takbeer in the hadith mentioned, what is meant by it is saying “Subhaan Allah, al-hamdu Lillah and Allahu akbar (Glory be to Allah, praise be to Allah, and Allah is Most Great)” thirty-three times after the prayer. In this way we can reconcile between the hadiths that have been narrated concerning this matter. End quote. 

Fataawa al-Lajnah ad-Daa’imah (5/420) 

Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) said: 

The Prophet (blessings and peace of Allah be upon him) used to recite the adhkaar out loud after the prayer. ‘Abdullah ibn ‘Abbaas (may Allah be pleased with him) said: The people at the time of the Prophet (blessings and peace of Allah be upon him) used to recite the dhikr out loud after the prayer. He also said: We only knew that the prayer of the Messenger of Allah (blessings and peace of Allah be upon him) had ended from the takbeer, i.e., from the takbeer that was recited with the dhikr, because the dhikr included saying “Subhaan Allah, al-hamdu Lillah and Allahu akbar (Glory be to Allah, praise be to Allah, and Allah is Most Great)”. End quote. 

Fataawa Noor ‘ala ad-Darb by al-‘Uthaymeen (8/2) 

For more information, please see also the answer to question no. 131850 

And Allah knows best.