210 (number)
210 (two hundred [and] ten) is the natural number following 209 and preceding 211.
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| Cardinal | two hundred ten | |||
| Ordinal | 210th (two hundred tenth) | |||
| Factorization | 2 × 3 × 5 × 7 | |||
| Divisors | 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210 | |||
| Greek numeral | ΣΙ´ | |||
| Roman numeral | CCX | |||
| Binary | 110100102 | |||
| Ternary | 212103 | |||
| Octal | 3228 | |||
| Duodecimal | 15612 | |||
| Hexadecimal | D216 | |||
In mathematics
210 is a composite number, an abundant number, and the product of the first four prime numbers (2, 3, 5, and 7), and thus a primorial. It is also the least common multiple of these four prime numbers. It is the sum of eight consecutive prime numbers (13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 = 210).[1]
It is a triangular number (following 190 and preceding 231), a pentagonal number (following 176 and preceding 247), and the second smallest to be both triangular and pentagonal (the third is 40755).[1]
It is also an idoneal number, a pentatope number, a pronic number, a Harshad number, and an untouchable number. 210 is also the first 71-gonal number, preceding 418.[1] It is the first primorial number greater than 2 which is not adjacent to 2 primes (211 is prime, but 209 is not).
It is the largest number n such that all primes between n/2 and n yield a representation as a sum of two primes.[2]
References
- Wells, D. (1987). The Penguin Dictionary of Curious and Interesting Numbers (p. 143). London: Penguin Group.
- Deshouillers, Jean-Marc; Granville, Andrew; Narkiewicz, Władysław; Pomerance, Carl (1993). "An upper bound in Goldbach's problem". Mathematics of Computation. 61 (203): 209–213. doi:10.1090/S0025-5718-1993-1202609-9.
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