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# 105 (number)

 ← 104 105 106 →
Cardinal one hundred five
Ordinal 105th
(one hundred fifth)
Factorization 3 × 5 × 7
Divisors 1, 3, 5, 7, 15, 21, 35, 105
Greek numeral ΡΕ´
Roman numeral CV
Binary 11010012
Ternary 102203
Quaternary 12214
Quinary 4105
Senary 2536
Octal 1518
Duodecimal 8912
Vigesimal 5520
Base 36 2X36

105 (one hundred [and] five) is the natural number following 104 and preceding 106.

## In mathematics

105 is a triangular number, a dodecagonal number[1] and the first Zeisel number.[2] It is a sphenic number, and is the product of three consecutive prime numbers. 105 is the double factorial of 7.[3] It is also the sum of the first five square pyramidal numbers.

105 comes in the middle of the prime quadruplet (101, 103, 107, 109). The only other such odd numbers less than a thousand are 9, 15, 195 and 825. 105 is also a pseudoprime 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 under the first definition.

105 is also a number n for which ${\displaystyle n-2^{k}}$ is prime, for ${\displaystyle 0. (This even works up to ${\displaystyle k=8}$, ignoring the negative sign.)

105 is the smallest integer such that the factorization of ${\displaystyle x^{n}-1}$ over Q includes coefficients other than ${\displaystyle \pm 1}$. In other words, the 105th cyclotomic polynomial, Φ105, is the first with coefficients other than ${\displaystyle \pm 1}$.

105 is also: