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fingers (digits).  

Other

See also: List of highways numbered 10

The number of kingdoms in Five Dynasties and Ten Kingdoms period.

The house number of 10 Downing Street.

The number of Provinces in Canada.

Number of dots in a tetractys.

The number of the French department Aube.

The number in tarot decks that corresponds to either Chance, Fortune, or the Wheel of Fortune, depending on the deck variant.[citation needed]

In mathematics

Ten is a composite number with 4 divisors, 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.[1]

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.

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.[2] 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,[3] and a tetrahedral number.[4]

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.

Ten factorial seconds is exactly equal to 6 weeks.

According to a conjecture, ten is the average sum of the proper divisors of the natural numbers if the size of the numbers approaches infinity (sequence A297575 in the OEIS).

Ten is the smallest number whose fourth power can be written as a sum of two squares in two different ways. (802 + 602 and 962 + 282)

In numeral systems

Decimal system

Main article: Decimal

As is the case for any base in its system, 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).

Roman numerals

The Roman numeral for ten is X (which looks like two Vs [the Roman numeral for 5] put together); it is thought that the V for five is derived from an open hand (five digits displayed), and X for ten from both hands. Incidentally, the Chinese word numeral for ten, is also a cross: 十.

Positional numeral systems other than decimal

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

Representation of 10 in other bases

BaseNumeral systemNumber

1unary

2binary1010

3ternary101

4quaternary22

5quinary20

6senary14

7septenary13

8octal12

9novenary11

10decimal10

12duodecimalX

16hexadecimalA

List of basic calculations

Multiplication12345678910  11121314151617181920  21 2225  501001000

10 × x102030405060708090100  110120130140150160170180190200  210220250  500100010000

Division12345678910  1112131415

10 ÷ x1053.32.521.61.4285711.251.11  0.900.830.7692300.7142850.6

x ÷ 100.10.20.30.40.50.60.70.80.91  1.11.21.31.41.5

Exponentiation12345678910

10x10100100010000100000100000010000000100000000100000000010000000000

x10110245904910485769765625604661762824752491073741824348678440110000000000

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