Kushina told naruto during the Madara & Hashirama battle that the 1st took control of the Kyuubi, now here is were the translation is unclear to me Mito Uzumaki sealed the Nine tail fox becoming the first 9 Tails Jinchūriki to better Aid Hashirama??? Is that during the fight with Madara or after???If it was during the fight i think they both ganged up on madara 2-1 giving the 1st the win.
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If they did both team up on Madara i don't think it was a 1 on 1 battle fair fight kushina stated that Mito was a strong female ninja on top of that born with particularlly strong chakra able to surpress the Kyuubi.
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Minato did mention that Madara wasn't able to keep the kyuubi control for a long time
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When Madara tryed summoning the Kyuubi he tolded naruto that he'd lend him his chakra to rather not be captured and be controlled by Madara again.
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So this is my theory about the Hashirama I think he's strong no doubt about it if he can go heads up with the uchiha clan but I think his fight with Madara was kind of over hyped if you ask me.This what i think what happen Madara & Hashirama were going at it Madara got frustrated and summoned the Nine tails but Hashirama was still putting up a fight. Mito arrives at the valley of end while Madara wasn't able to keep the kyuubi under control much longer so the kyuubi was
A. Took under control by the 1st hokage sealed into Mito and help Hashirama win the fight.
B. Kyuubi was no longer under control knowing that he hated Madara he team up with Hashirama to fight Madara then got duke and sealed after.
C. Kyuubi was no longer under control under madara then was take over by the Hashirama during the fight
The Battle of Madara Vs Hashirama is too unclear to me so i'm going with Itachi