105 is the natural number

Natural number

In mathematics, the natural numbers are the ordinary whole numbers used for counting and ordering . These purposes are related to the linguistic notions of cardinal and ordinal numbers, respectively...

 following 104

104 (number)

104 is the natural number following 103 and preceding 105.- In mathematics :One hundred [and] four is a primitive semiperfect number and a composite number, with its divisors being 1, 2, 4, 8, 13, 26, 52 and 104. As it has 8 divisors total, and 8 is one of those divisors, 104 is a refactorable...

 and preceding 106

106 (number)

106 is the natural number following 105 and preceding 107.-In mathematics:106 is the thirty-first distinct biprime and the fifteenth of the form...

.

In mathematics

105 is a triangular number

Triangular number

A triangular number or triangle number numbers the objects that can form an equilateral triangle, as in the diagram on the right. The nth triangle number is the number of dots in a triangle with n dots on a side; it is the sum of the n natural numbers from 1 to n...

, a 12-gonal number

Polygonal number

In mathematics, a polygonal number is a number represented as dots or pebbles arranged in the shape of a regular polygon. The dots were thought of as alphas . These are one type of 2-dimensional figurate numbers.- Definition and examples :...

 and a Zeisel number. It is a sphenic number

Sphenic number

In number theory, a sphenic number is a positive integer which is the product of three distinct prime numbers.Note that this definition is more stringent than simply requiring the integer to have exactly three prime factors; e.g. 60 = 22 × 3 × 5 has exactly 3 prime factors, but is not sphenic.All...

, and is the product of three consecutive prime number

Prime number

A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. A natural number greater than 1 that is not a prime number is called a composite number. For example 5 is prime, as only 1 and 5 divide it, whereas 6 is composite, since it has the divisors 2...

s. 105 is the double factorial of 7. It is also the sum of the first five square pyramidal number

Square pyramidal number

In mathematics, a pyramid number, or square pyramidal number, is a figurate number that represents the number of stacked spheres in a pyramid with a square base...

s.

105 comes in the middle of the prime quadruplet (101, 103, 107, 109). The only other such odd numbers less than a thousand are 15, 195 and 825. 105 is also a pseudoprime

Pseudoprime

In number theory, the Fermat pseudoprimes make up the most important class of pseudoprimes that come from Fermat's little theorem.- Definition :...

 to the prime bases 13, 29, 41, 43, 71, 83 and 97. The distinct prime factors of 105 add up to 15, and so do those of 104, hence the two numbers form a Ruth-Aaron pair

Ruth-Aaron pair

In mathematics, a Ruth–Aaron pair consists of two consecutive integers for which the sums of the prime factors of each integer are equal:andIf only distinct prime factors are counted, the first few Ruth–Aaron pairs are:...

 under the first definition.

105 is also a number n for which is prime, for . (This even works up to , ignoring the negative sign.)

105 is the smallest integer such that the factorization of over Q includes coefficients other than .

In other fields

105 is also:

• The number of sura
  Sura
  A sura is a division of the Qur'an, often referred to as a chapter. The term chapter is sometimes avoided, as the suras are of unequal length; the shortest sura has only three ayat while the longest contains 286 ayat...
  
  t al-Fil in the Qur'an
  Qur'an
  The Quran , also transliterated Qur'an, Koran, Alcoran, Qur’ān, Coran, Kuran, and al-Qur’ān, is the central religious text of Islam, which Muslims consider the verbatim word of God . It is regarded widely as the finest piece of literature in the Arabic language...
  
  .
• A simple card game where players lose if they have over 105 points.