Divergent Factions and Hogwarts Houses: The Similarities and Differences

In the world of Divergent, there are five different factions. Dauntless the brave, Erudite the intelligent, Amity the peaceful, Candor the honest and Abnegation the selfless. At Hogwarts school of Witchcraft and Wizardry (I've just started my fourth year there by the way), there are four houses. Gryffindor for the brave and chivalrous, Ravenclaw for the wise, Slytherin for the cunning and Hufflepuff for the loyal and hardworking. There are many similarities between these two systems of sorting that are immediately apparent, and I am going to list them here.
But before I begin, I'd like to say that though it may seem as if all Dauntless are Gryffindors and all Ravenclaws are Erudite, the faction and house systems are much too complex to simply say "all people in this house are in that faction". For instance, both Erudite and Ravenclaw value intelligence, but where as Erudite is obsessed with being knowledgeable and collecting facts, Ravenclaw is more concerned with being clever and creative. Many people who are in Erudite are actually Slytherin, not Ravenclaw and many people who are Ravenclaw are Candor or even Amity.
Similarly, not all Gryffindors are Dauntless. While Gryffindors are known to be loyal and true to their friends, Dauntless is more about doing dangerous and impressive things just for the fun of it. For this reason, I believe that many Dauntless are actually Slytherin and many Gryffindors are actually Abnegation.
So, as you can see, connecting the Hogwarts Houses and the Divergent Factions is actually much more complicated than it seems at first.

Here is a list of what I believe to be the similarities between the houses and the factions:

If you are Dauntless, you will most likely be a Gryffindor or Slytherin.
If you are Erudite you will probably be in Slytherin or Ravenclaw.
People who are Amity will usually be Hufflepuff.
Those in Abnegation will most likely be a Gryffindor or a Hufflepuff.
If you are Candor you could be in any house but Slytherin.

Gryffindors will usually be Dauntless or Abnegation, though some will be in Candor. It's pretty rare to have an Amity or Erudite Gryffindor, but not unheard of.
Ravenclaws will almost always be Erudite though many will be Candor. It is also entirely possible to be a Dauntless, Abnegation or Amity Ravenclaw too.
Hufflepuffs will be evenly spread throughout Amity, Abnegation and Candor. It would be pretty rare to be a Dauntless or Erudite Hufflepuff, but it is possible.
Those in Slytherin will almost always be either Dauntless or Erudite. I honestly can't imagine a Candor Slytherin. It's even harder to imagine one in Amity or Abnegation.