I have heard there is a hadith about 73 sects from Ibn Majah. I want to know the authenticity of this hadeeth. Please give me some reasons to prove this hadeeth as sahih.
The hadith you are referring to is authentic, and has multiple versions with different grades.
It was compiled in Jami' at-Tirmidhi hadiths 2640 and 2641, Sunan Abi Dawud hadiths 4596 and 4597, Sunan Ibn Majah hadiths 3991 and 3992 and 3993, Musnad Ahmad hadith 2/332, Al-Mustadrak hadith 61, as well as numerous other books of hadith.
The hadith was narrated with essentially two versions through the authority of multiple companions:
- 'Abdullah ibn 'Amr ibn al-'As
- 'Abdullah ibn Mas'ud
- Abu Hurairah
- Abu Musa al-Ash'ari
- Abu Umamah al Bahili
- Abu al-Darda'
- 'Ali ibn Abi Talib
- 'Amr ibn Awf
- Anas ibn Malik
- 'Awf ibn Malik
- Jaber bin 'Abdullah
- Mu'awiyah ibn Abu Sufyan
- Sa'd ibn Abi Waqqas
- Wathela ibn al-Asqa'
The first version mentions that the Muslim nation will be divided into 73 sects and mention that only one sect will be saved:
عَنْ أَنَسِ بْنِ مَالِكٍ، قَالَ قَالَ رَسُولُ اللَّهِ ـ صلى الله عليه وسلم ـ إِنَّ بَنِي إِسْرَائِيلَ افْتَرَقَتْ عَلَى إِحْدَى وَسَبْعِينَ فِرْقَةً وَإِنَّ أُمَّتِي سَتَفْتَرِقُ عَلَى ثِنْتَيْنِ وَسَبْعِينَ فِرْقَةً كُلُّهَا فِي النَّارِ إِلاَّ وَاحِدَةً وَهِيَ الْجَمَاعَةُ
It was narrated from Anas bin Malik that the Messenger of Allah (ﷺ) said: The Children of Israel split into seventy-one sects, and my nation will split into seventy-two, all of which will be in Hell apart from one, which is the main congregation.
The second version mentions that the Muslim nation will be divided into 73 sects only, with no mention of the sect that will be saved:
عَنْ أَبِي هُرَيْرَةَ قَالَ: قَالَ رَسُولُ اللَّهِ صلى الله عليه وسلم: افْتَرَقَتِ الْيَهُودُ عَلَى إِحْدَى أَوْ ثِنْتَيْنِ وَسَبْعِينَ فِرْقَةً وَتَفَرَّقَتِ النَّصَارَى عَلَى إِحْدَى أَوْ ثِنْتَيْنِ وَسَبْعِينَ فِرْقَةً وَتَفْتَرِقُ أُمَّتِي عَلَى ثَلاَثٍ وَسَبْعِينَ فِرْقَةً
Narrated AbuHurayrah: The Prophet (ﷺ) said: The Jews were split up into seventy-one or seventy-two sects, and the Christians were split up into seventy-one or seventy-two sects, and my community will be split up into seventy-three sects.
Note that sect is referring to groups that will differ in their creed ('Aqīda, Arabic: العقيدة). Groups that differ on branches of practice are called jurisprudence schools (madhhab, Arabic: مذهب).
For more information, you may refer to this discussion (Arabic only). Tne reason the hadith is authentic through some of its chains is that the entire chain is trustworthy, of good memory, and continuous.
Althought you've already received a more-than-exhaustive answer, I'd like to add that it is authentic for current circumstances amongst Muslims in terms of Aqeedah as well. You can clearly see many arguments amongst Muslim groups who hate one another.