Number

The "Numbers" are a set of 100 Xyz Monsters that are included in the show Yu-Gi-Oh! ZEXAL. Supposedly pieces of the mysterious entity Astral, the protagonist of the show, Yuma Tsukumo, must acquire all 100 and solve the mysteries behind these powerful creatures.

Description
Here is the information regarding the Numbers, in both the canon series, and in other stories in other universes.

ZEXAL
When Yuma Tsukumo unlocked the Door with his Emperor's Key, he opened a portal between his own dimension and another, allowing Astral to come into his world. Yuma found himself trapped within a sphere of blank cards, which shortly shattered away. By crossing into Yuma's world, Astral's memories got transformed into the hundred "Number" cards and scattered in unknown directions. In order to regain his lost memories, Astral teamed up with Yuma. When they are Summoned, their respective numbers are printed on their users. They have been shown to be very dangerous, as their users are easily possessed by their power (with the exception of Yuma due to his partnership with Astral and Kaito who has powers similar to those of Astral's). It is said that these "Number" monsters cannot be destroyed with cards in this world. "Number" monsters can only be defeated by other "Number" monsters. However, when two or more "Numbers" confront themselves in a Duel they'll fight each other to consume one another. When a "Number" is defeated in a Duel by Yuma, Yuma obtains it, and its power is absorbed into Astral. Also when Yuma defeats a "Number" monster Astral gains another part of his memory. Astral mentions there are 99 Numbers, but according to Kaito Tenjo, there are 100 Numbers. As Astral already had 1 of the Numbers, "Utopia", it is possible Astral was referring to the other 99 Numbers.

Abilities
In the anime, "Numbers" have a few "special" abilities that are unique. "Numbers" can only be destroyed by other "Numbers". The "Numbers" amplify the darkness and desires of humans, whether these cause good or bad. When a "Number" is defeated, they are absorbed into Astral, and can be used by any duelist whom Astral is currently with. Each "Number" contains a piece of Astral's memory, which he recovers each time he absorbs one. They are also known to manipulate their user into summoning them as soon as possible, sometimes to the point of cheating as seen with Rikuo and Kaio. Numbers also manipulate their users into protecting them at any cost, as seen when "Number 83: Galaxy Queen" made Fuya Okudaira believe that she was his mother. Thus, he equipped her with "Cursed Seal of Dead Max" to protect her from being destroyed by battle, and changed the attack target to his "D.D. ESPer Star Robin" via "Star Robin is Forever!", causing him to lose the Duel. A person possessed by a "Number" easily becomes addicted to their power and desires to obtain more "Numbers". It is, however, possible for some people to resist this effect, at least temporarily, as Tetsuo Takeda managed to do when he used Number 39: Utopia to save Yuma from "Number 96: Black Mist". Interestingly, whenever a "Number" is Xyz Summoned, they initially appear as a strange object, what is possibly a sealed form, until they transform into the actual monster and gain their Number on their bodies.

Alternate Numbers
However, there are also alternate Numbers from other universes. In some realities, these Numbers have replaced other Numbers from the original Duel Monsters universe. For example, in one alternate reality, Kotori, Yuma's love interest, gains Number 13: Paradise to help out Number 39: Utopia. Plus, some duelists are able to control normal Numbers as well without having the Number take them over, such as Chris Muir, who has Number 48: XX-Saber Twinbladeknight and Number 66: X-Saber Bariza. Since these Numbers are from different universes, some Numbers in one reality will be completely different Numbers in others, allowing for different cards to have the same Number.

Subtypes
Furthermore, there are several different subsets of the Numbers, which will be described below.

Chaos Numbers
The "Chaos Numbers" are a new set of Xyz Monsters recently introduced in ZEXAL. They seem to be upgrades of Numbers, but how and why is not yet certain. All that is known is that they can use the previous Number as an Xyz Material, along with the previous Number's materials, have special support monsters called "Zexal Weapons", and have rather powerful effects that can only be activated at certain times of the duel.

Cross Chaos Numbers
The "Cross Chaos Numbers" add on to the power of "Chaos Numbers" by combining two or more "Numbers" into a unified monster. The ATK and DEF of the "Cross Chaos Number" is the total ATK and DEF of the original "Numbers" used, but 1000 is subtracted for each of the original "Numbers", and their Ranks and Number are calculated by adding the Number and Rank of the original "Numbers" together (though a Number cannot exceed 12 in its Rank). Each "Cross Chaos Number" has 2 effects that use Xyz Materials. One effect is a combination of the effects of the original Numbers, usually being once per turn and using only 1 Xyz Material, while the other uses many Xyz Materials in one move, and doing something for each Xyz Material removed. Finally, a "Cross Chaos Number", when it leaves the field, can Special Summon one of the "Numbers" used to Xyz Summon it from the Graveyard and attach itself to that "Number" as an Xyz Material.

Multiplication Numbers
The "Multiplication Numbers" are an upgraded style of Numbers introduced in a fic taking place in the future of ZEXAL. Yuko Tsukumo, daughter of Yuma and Kotori, has the ability to use the ZEXAL power to combine two Numbers into one being in dire situations. The Numbers of these monsters are the products of their Fusion Materials' Numbers. Despite being Fusion Monsters, they have Ranks, as they are Fusions of 2 (or sometimes 3) Xyz Monsters, the product of which is a special type of Fusion Monster called a "Fuxyz Monster". One such Number is "Number 663: Leviathan Rider Utopia," which combines the offensive abilities of "" and the defensive abilities of "". It is theorized that "Multiplication Numbers" were created from the concept of "Cross Chaos Numbers", similar to how Synchro Monsters (and eventually Xyz Monsters) were spawned from the idea of.

Factorial Numbers
The "Factorial Numbers" are a semi-related subset of Numbers, consisting of one Xyz Monster from each Type, which all of them either belong to or support a popular Archetype, be it canon or original. They have been scattered across the Duel Monsters multiverse by the enigmatic entity Protsu, and will be used by both DATEA, an evil organization wishing to conquer all universes, and those few that are fighting to free the Duel Monsters multiverse from DATEA's slowly-strengthening grip. The Factorial Numbers are said to be fragments of...

Irrational Numbers
The "Irrational Numbers", also called "Remote Dragons", are 6 legendary dragons, one of each Attribute, that were the guardians of the Architects' home universe. Since the demise of the dimensional-spanning civilization, these cards have been scattered to the four winds across the Duel Monsters multiverse, but the Factorial Numbers will be used to find these legendary monstrosities and revive them, allowing the holders to either save the Duel Monsters multiverse, or enslave it. The Irrational Numbers are all high-Rank Xyz Monsters with the same effect their anime counterparts have, as well as incredibly powerful effects that can easily change the outcome of the duel in the favor of the user.

Lost Numbers
Finally, there are the "Lost Numbers", a very small group of Xynchro Monsters. All of them are "00", and they all have more specific requirements than "Multinetwork God Yotta Byte". However, they are very few and very far between, though their power is quite impressive. The only one known of, "Lost Number 00: Biobeast Zonoid", is virtually unstoppable with an unnegatable negation ability.