An extract on #10
A collection of ten items (most often ten years) is called a decade.
The ordinal adjective is decimal; the distributive adjective is denary.
Increasing a quantity by one order of magnitude is most widely understood to mean multiplying the quantity by ten.
To reduce something by one tenth is to decimate. (In ancient Rome, the killing of one in ten soldiers in a cohort was the punishment for cowardice or mutiny; or, one-tenth of the able-bodied men in a village as a form of retribution, thus causing a labor shortage and threat of starvation in agrarian societies.)
A theoretical highest number in topics that require a rating ("a mark out of ten"), by contrast having 0 or 1 as the lowest number, and 5 being average.
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 (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.
Ten is the smallest semiprime that is the sum of all the distinct prime numbers from its lower factor through its higher factor (10 = 2 + 3 + 5 = 2 . 5) Only three other small semiprimes (39, 155, and 371) share this attribute.
Ten is a semi-meandric number.
Ten is the sum of the first three prime numbers, of the four first positive integers (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. Because 10 is the product of a power of 2 (namely 21) with nothing but distinct Fermat primes (specifically 5), a regular decagon is a constructible polygon.
Ten is also a triangular number, a centered triangular number, and a tetrahedral number.
Ten is the number of n queens problem solutions for n = 5.
Ten is the smallest number whose status as a possible friendly number is unknown.