Hidan and Kakuzu were probably the best functioning team within the Akatsuki. That wasn't to say that they got along the best, or were the closest, or were even the most skilled. Hidan had the slowest attack speed of anyone in the organization, and the worst aim. Kakuzu had uncontrollable bloodlust that made him a danger to anyone he worked with, spoke to, or occupied the same space as.
Hidan was a foul-mouthed, bratty, whiner with a God-complex as wide as the heavens, and more annoying than if it was his own God-complex he was a God-complex. There never was anyone as devoted to their religion as Hidan, and he took up the better part of both his and his partner's time with his absurd and lengthy rituals. Kakuzu might have found them hilarious, if they weren't so boring. Honestly, he could only stare at a man impaled through the chest for so long before it wasn't funny anymore, and just irritating, and he never thought he'd think that about gore.
Kakuzu was a cheap, money-hungry, murderous bastard who had no care for anyone save for himself, and just how much currency he could fit inside the generous pockets of his robe. He hadn't been elected or even considered for the position of Treasurer of the Akatsuki; he had earned the title simply because bounties were his passion. He salivated at the thought of paper money crinkling between his fingers, and the sound of coins in his palm got him giddy. Hidan was a little sickened by someone who fawned over cash the way Kakuzu did (this coming from a zealot, of all people), the way he worshiped and chased after money, so totally hypnotized by it. Hidan didn't think he'd ever seen so in need of a good fuck in his entire life.
So, no, they didn't really belong together; not from that standpoint, anyway. Kakuzu had a notoriously short temper, and Hidan really liked to piss him off—they were a horrible match, in any case, save for one:
They couldn't die.
More specifically Hidan couldn't die, Kakuzu was just a pain in the ass to kill. The real key to their phenomenal teamwork was that Kakuzu, the "real doer" as Hidan called him, could attack however he pleased whenever he pleased, and never had to spare a second thought for his companion's welfare. In fact most of their battle strategies involved them attacking at the same time, Kakuzu attacking right through Hidan, the silver-haired man completely unaffected.
It was a partnership born from convenience. Kakuzu had the nasty habit of slaughtering all his comrades, and Hidan was immortal. This was Kakuzu's point of view, anyway. Hidan found the greatest convenience to be that when any given piece of him got lopped off Kakuzu could sew it back on. Like amputation waiting to happen, Hidan constantly relied on his giant walking spool of thread.
Ah, compatriotism. It warmed two of Kakuzu's five hearts.