# Ten

## Etymology

Middle English, from Old English tīene, from tīen, adjective, ten; akin to Old High German zehan ten, Latin decem, Greek deka

- Date: before 12th century

## Definitions

- 1 : the 10th in a set or series <wears a ten>
- 2 : something having 10 units or members
- 3 : a 10-dollar bill
- 4 : one deserving the highest rating; specifically : an exceptionally attractive person

## Description

10 (ten) is an even natural number following 9 and preceding 11.

## In mathematics

**Ten** is a composite number, its proper divisors being 1, 2 and 5. Ten is the smallest noncototient, a number that cannot be expressed as the difference between any integer and the total number of coprimes below it.

Ten is the second discrete semiprime (2.5) and the second member of the (2.q) discrete semiprime family. Ten has an aliquot sum σ(n) of 8 and is accordingly the first discrete semiprime to be in deficit. All subsequent discrete semiprimes are in deficit. The aliquot sequence for 10 comprises five members (10,8,7,1,0) with this number being the second composite member of the 7-aliquot tree.

It is the aliquot sum of only one number the discrete semiprime 14.

Ten is a semi-meandric number.

Ten is the sum of the first three prime numbers, of the four first numbers (1 + 2 + 3 + 4), of the square of the two first odd numbers and also of the first four factorials (0! + 1! + 2! + 3!). Ten is the eighth Perrin number, preceded in the sequence by 5, 5, 7.

A polygon with ten sides is a decagon, and 10 is a decagonal number. But it is also a triangular number and a centered triangular number.

Ten is the number of n-Queens Problem solutions for n = 5.

## In numeral systems

Ten is the base of the decimal numeral system, by far the most common system of denoting numbers in both spoken and written language. Ten is the first two-digit number in decimal and thus the lowest number where the position of a numeral affects its value. Any integer written in the decimal system can be multiplied by ten by adding a zero to the end (e.g. 855 * 10 = 8550). The reason for the choice of ten is assumed to be that humans have ten fingers (digits).

The digit '1' followed by '0' is how the value of p is written in base p. (E.g. 16 in hexadecimal is 10.)

The Roman numeral for ten is X (which looks like two V's [the Roman numeral for 5] put together); it is thought that the V for five is derived from an open hand (five digits displayed). The Chinese word numeral for ten is 十, which resembles a cross.