| ||||
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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
[edit]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 () and is less than the square of the next prime (11) by > 8. Therefore, for , 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 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 non-zero coefficients other than . In other words, the 105th cyclotomic polynomial, Φ105, is the first with coefficients other than .
105 is the number of parallelogram polyominoes with 7 cells.[4]
In science
[edit]- The atomic number of dubnium.
In other fields
[edit]105 is also:
- A Shimano Road groupset since 1984
See also
[edit]References
[edit]- Wells, D. The Penguin Dictionary of Curious and Interesting Numbers London: Penguin Group. (1987): 134
- ^ "Sloane's A051624 : 12-gonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-27.
- ^ "Sloane's A051015 : Zeisel numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-27.
- ^ "Sloane's A006882 : Double factorials". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-27.
- ^ Sloane, N. J. A. (ed.). "Sequence A006958 (Number of parallelogram polyominoes with n cells (also called staircase polyominoes, although that term is overused))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
Well, that’s interesting to know that Psilotum nudum are known as whisk ferns. Psilotum nudum is the commoner species of the two. While the P. flaccidum is a rare species and is found in the tropical islands. Both the species are usually epiphytic in habit and grow upon tree ferns. These species may also be terrestrial and grow in humus or in the crevices of the rocks.
View the detailed Guide of Psilotum nudum: Detailed Study Of Psilotum Nudum (Whisk Fern), Classification, Anatomy, Reproduction