Does uttering "Allahu Akbar" once necessitate the mentioned reward, or must it be repeated 100 times to obtain it?

What you heard about the فضl (virtue) of saying "Allahu Akbar" is true. It was reported in a Hadith narrated by Imam Ahmad and others, and authenticated by a number of scholars. Its wording is: "Indeed, Allah the Almighty chose four phrases from speech: 'SubhanAllah (Glorified is Allah),' 'Alhamdulillah (All praise is due to Allah),' 'La ilaha illa Allah (There is no god but Allah),' and 'Allahu Akbar (Allah is the Greatest).' Whoever says 'SubhanAllah,' twenty good deeds will be written for him, and twenty sins will be removed from him. And whoever says 'Allahu Akbar,' the same applies. And whoever says 'La ilaha illa Allah,' the same applies. And whoever says 'Alhamdulillah Rabb al-Alamin (All praise is due to Allah, Lord of the worlds)' from his own accord, thirty good deeds will be written for him, and thirty sins will be removed from him." So, if one says "Allahu Akbar" once, twenty good deeds will be written for him, and twenty sins will be removed from him.

It is stated in Tafsir al-Qurtubi that "Allahu Akbar" is the most eloquent phrase for Arabs in conveying the meaning of glorification and majesty, meaning describing Allah as greater than everything. The Prophet, peace and blessings be upon him, used to say "Allahu Akbar" when he entered into prayer. And Umar ibn al-Khattab said: "A servant's saying 'Allahu Akbar' is better than the world and what is in it."