10

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10 (ten) is the even natural number following 9 and preceding 11. Ten is the base of the decimal numeral system, the most common system of denoting numbers in both spoken and written language.

Ten is the fifth composite number, and the smallest noncototient, which is a number that cannot be expressed as the difference between any integer and the total number of coprimes below it.^[1] Ten is the eighth Perrin number, preceded by 5, 5, and 7.^[2]

The factorial of ten is equal to the product of the factorials of the first four odd numbers as well: ,^[8] and 10 is the only number whose sum and difference of its prime divisors yield prime numbers and .${\displaystyle 10!=1!\cdot 3!\cdot 5!\cdot 7!}$${\displaystyle (2+5=7}$${\displaystyle 5-2=3)}$

Ten has an aliquot sum of 8, and is the first discrete semiprime to be in deficit, as with all subsequent discrete semiprimes.^[9] It is the second composite in the aliquot sequence for ten (10, 8, 7, 1, 0) that is rooted in the prime 7-aliquot tree.^[10]${\displaystyle (2\times 5)}$

According to conjecture, ten is the average sum of the proper divisors of the natural numbers if the size of the numbers approaches infinity,^[11] and it is the smallest number whose status as a possible friendly number is unknown.^[12]${\displaystyle \mathbb {N} }$

Figurate numbers that represent regular ten-sided polygons are called decagonal and centered decagonal numbers.^[14] On the other hand, 10 is the first non-trivial centered triangular number^[15] and tetrahedral number.^[16][b]

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