105 (number)

← 104 105 106 →
← 100 101 102 103 104 105 106 107 108 109 → List of numbers; Integers; ← 0 100 200 300 400 500 600 700 800 900 →
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
Senary	2536
Octal	1518
Duodecimal	8912
Hexadecimal	6916

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 the first odd 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 numbers less than a thousand are 9, 15, 195, and 825.

105 is also the middle of the only prime sextuplet (97, 101, 103, 107, 109, 113) between the ones occurring at 7-23 and at 16057–16073. 105 is the product of the first three odd primes ( $3\times 5\times 7$ ) and is less than the square of the next prime (11) by > 8. Therefore, for $n=105$ , n ± 2, ± 4, and ± 8 must be prime (a prime k-tuple). In contrast, n ± 6, ± 10, ± 12, and ± 14 must be composite, making a prime gap on either side.

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 $0<k<log_{2}(n)$ . (This even works up to $k=8$ , ignoring the negative sign.)

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