9814072356 (number)
9814072356 or 9,814,072,356 is 99066 squared, and is the eighty-seventh and largest square number
Square number
In mathematics, a square number, sometimes also called a perfect square, is an integer that is the square of an integer; in other words, it is the product of some integer with itself...

 using each of the digits 1, 2, 3, 4, 5, 6, 7, 8, 9, and 0 exactly once .
List of numbers - Integers

1000000000 (number)
1,000,000,000 is the natural number following 999,999,999 and preceding 1,000,000,001.In scientific notation, it is written as 109....

   9814072356   10000000000
Cardinal number
In mathematics, cardinal numbers, or cardinals for short, are a generalization of the natural numbers used to measure the cardinality of sets. The cardinality of a finite set is a natural number – the number of elements in the set. The transfinite cardinal numbers describe the sizes of infinite...

Ordinal number
In set theory, an ordinal number, or just ordinal, is the order type of a well-ordered set. They are usually identified with hereditarily transitive sets. Ordinals are an extension of the natural numbers different from integers and from cardinals...

In mathematics, factorization or factoring is the decomposition of an object into a product of other objects, or factors, which when multiplied together give the original...

Binary numeral system
The binary numeral system, or base-2 number system, represents numeric values using two symbols, 0 and 1. More specifically, the usual base-2 system is a positional notation with a radix of 2...

In mathematics and computer science, hexadecimal is a positional numeral system with a radix, or base, of 16. It uses sixteen distinct symbols, most often the symbols 0–9 to represent values zero to nine, and A, B, C, D, E, F to represent values ten to fifteen...


More generally, it is also the largest distinct-digit perfect power being the 657th such number . Note that the digital root
Digital root
The digital root of a number is the value obtained by an iterative process of summing digits, on each iteration using the result from the previous iteration to compute a digit sum...

 of both 9814072356 and 657 is 9.

It is the square of the third largest 5-digit strobogrammatic number
Strobogrammatic number
A strobogrammatic number is a number that, given a base and given a set of glyphs, appears the same whether viewed normally or upside down. In base 10, given a set of glyphs where 0, 1 and 8 are symmetrical around the horizontal axis, and 6 and 9 are the same as each other upside down , the first...

 (99866 and 99166 being larger).

It is also a member of , the sequence of perfect powers where all neighbouring digits are distinct.

All the prime digits are adjacent 7,2,3,5 in a cycle
Cycle (mathematics)
In mathematics, and in particular in group theory, a cycle is a permutation of the elements of some set X which maps the elements of some subset S to each other in a cyclic fashion, while fixing all other elements...

, which is equal to the cycle {2357} of the natural order.

9814072356 is a permutation
In mathematics, the notion of permutation is used with several slightly different meanings, all related to the act of permuting objects or values. Informally, a permutation of a set of objects is an arrangement of those objects into a particular order...

: of order 10 read left to right, and of order 6 ({9},{8},{2,3},{0,6,4,7,1,5}) read right to left.

In base 2 and 3 its last 6 digits are the same (100100).
The source of this article is wikipedia, the free encyclopedia.  The text of this article is licensed under the GFDL.