“I once complained to Rasulullah (ﷺ) that I hear many Ahadeeth from you but I forget them. Rasulullah (ﷺ) said to me, ‘Spread out your shawl!’ So I spread it out. He (ﷺ) made some signs on the shawl with his own Mubarak hands. Then he (ﷺ) said, ‘Now wrap this shawl around you!’ So I wrapped around me and I never forgot anything after that.” (Bukhari #119, Tirmizi #3835)
Once Hazrat Abu Hurayrah (Radiyallahu Anhu) narrated the following Hadeeth:

“A person participating in a Janazah Salah gets one Qeeraat of reward if he returns after the Janazah Salah, but gets two Qeeraats of reward if he remains there till the burial is over, and one Qeeraat is weightier than Mount Uhud.”

Hazrat Abdullah bin Umar (Radiyallahu Anhuma) heard this and doubted the authenticity of the Hadeeth, saying: “O Abu Hurayrah! Think before you speak.”

Hazrat Abu Hurairah (Radiyallahu Anhu) got upset over this and took Hazrat Abdullah bin Umar (Radiyallahu Anhuma) to Hazrat Aisha (Radiyallahu Anha) and said to her: “O Ummul Mu’mineen, I request you to say by Allah if you have heard from Rasulullah (ﷺ) the Hadeeth regarding the qeeraats of reward?” She replied: “Yes. I have heard this Hadeeth.” (Saheeh Muslim #945/6)

Hazrat Abu Hurayrah (Radiyallahu Anhu) then said to Hazrat Abdullah bin Umar (Radiyallahu Anhuma): “During the time of Rasulullah (ﷺ), I had no tree to plant in the orchard and no merchandise to sell in the market. I was always with Rasulullah (ﷺ). My only job was to memorise what Rasulullah (ﷺ) said, and to eat only what he gave me.”

Hazrat Abdullah bin Umar (Radiyallahu Anhuma) acknowledged this and said: “No doubt. Of us all, you most constant in attendance to him and therefore most informed about Rasulullah (ﷺ).” (Tirmizi #3836)
Once a man said to Hazrat Talha bin Ubaydillah (Radiyallahu Anhu) and asked him, “O Abu Muhammad! Have you seen this Yemeni (i.e. Hazrat Abu Hurayrah Radiyallahu Anhu), is he more knowledgeable than you’ll regarding the Ahadeeth of Rasulullah (ﷺ)? We hear from him what we do not hear from you’ll or is he saying that which Rasululllah (ﷺ) did not say?” Hazrat Talha (Radiyallahu Anhu) replied, “As for him hearing that which we did not hear from Rasulullah (ﷺ), that was he because he was destitute, owned nothing and was the guest of Rasulullah (ﷺ). His hand was with the hand of Rasulullah (ﷺ). We had homes and wealth. We used to come to Rasulullah (ﷺ) at the two ends of the day. I have no doubt that he heard from Rasulullah (ﷺ) what we did not hear. And you will not find any good in anyone who attributes anything to Rasulullah (ﷺ) that which he did not say. (Tirmizi #3837)
Hazrat Abu Hurayrah (Radiyallahu Anhu) once said, “No one has narrated more about Rasulullah (ﷺ) than me, except Hazrat Abullah ibn Amr (Radiyallahu Anhuma). This is because he used write down (what he heard) whilst I would not write (I would rely on my memory).” (Bukhari #113,Tirmizi #3841)
However, the narrations of Hazrat Abdullah ibn Amr (Radiyallahu Anhuma) are not as famous. This was because he did not remain in Madeenah Munawwah – he went to Taif – whilst Hazrat Abu Hurayrah (Radiyallahu Anhu) remained in Madeenah and thus had more students. Approximately 800 people narrate Hadeeth from him.
Once Marwan ibn al-Hakam wanted to test Hazrat Abu Hurayrah's (Radiyallahu Anhu) power of memory. He sat with him in one room and behind a curtain he placed a scribe, unknown to Hazrat Abu Hurayrah (Radiyallahu Anhu), and ordered him to write down whatever Abu Hurayrah (Radiyallahu Anhu) said. A year later, Marwan called Hazrat Abu Hurayrah (Radiyallahu Anhu) again and asked him about the same Ahadith which the scribe had recorded. It was found that he had forgotten not a single word. (Hayatus Sahabah)