105 (number)

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

← 104 106 → 105
← 100 101 102 103 104 105 106 107 108 109 → List of numbers — Integers ← 100 110 120 130 140 150 160 170 180 190 →
Cardinal	one hundred [and] five
Ordinal	105th (one hundred [and] fifth)
Numeral system	105
Factorization	$3 \cdot 5 \cdot 7$
Divisors	1, 3, 5, 7, 15, 21, 35, 105
Roman numeral	CV
Binary	11010012
Octal	1518
Duodecimal	8912
Hexadecimal	6916

In mathematics

105 is a triangular number, a 12-gonal number and a Zeisel number. It is a sphenic number, and is the product of three consecutive prime numbers. 105 is the double factorial of 7. 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 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 n − 2^k is prime, for 0 < k < log₂(n). (This even works up to k = 8, ignoring the negative sign.)

105 is the smallest integer such that the factorization of xⁿ − 1 over Q includes coefficients other than $\pm 1$.

In science

• The atomic number of hahnium, also known as dubnium.

In other fields

105 is also:

• The number of surat al-Fil in the Qur'an.^{[citation needed]}
• A simple card game where players lose if they have over 105 points.

See also

• List of highways numbered 105

References

• Wells, D. The Penguin Dictionary of Curious and Interesting Numbers London: Penguin Group. (1987): 134