# 105 (number)

 ← 104 105 106 →
Cardinalone hundred five
Ordinal105th
(one hundred fifth)
Factorization3 × 5 × 7
Divisors1, 3, 5, 7, 15, 21, 35, 105
Greek numeralΡΕ´
Roman numeralCV
Binary11010012
Ternary102203
Octal1518
Duodecimal8912

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 non-zero 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:

## References

1. ^ "Sloane's A051624 : 12-gonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-27.
2. ^ "Sloane's A051015 : Zeisel numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-27.
3. ^ "Sloane's A006882 : Double factorials". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-27.