← 209 210 211 →
Cardinaltwo hundred ten
Ordinal210th
(two hundred tenth)
Factorization2 × 3 × 5 × 7
Divisors1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210
Greek numeralΣΙ´
Roman numeralCCX
Binary110100102
Ternary212103
Senary5506
Octal3228
Duodecimal15612

210 (two hundred [and] ten) is the natural number following 209 and preceding 211.

Mathematics

210 is an abundant number,[1] and Harshad number. It is the product of the first four prime numbers (2, 3, 5, and 7), and thus a primorial,[2] where it is the least common multiple of these four prime numbers. 210 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 sum of eight consecutive prime numbers, between 13 and the thirteenth prime number: 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 = 210.[3]

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).[3]

It is also an idoneal number, a pentatope number, a pronic number, and an untouchable number. 210 is also the third 71-gonal number, preceding 418.[3]

210 is index n = 7 in the number of ways to pair up {1, ..., 2n} so that the sum of each pair is prime; i.e., in {1, ..., 14}.[4][5]

It is the largest number n where the number of distinct representations of n as the sum of two primes is at most the number of primes in the interval [n/2 , n − 2].[6]

Integers between 211 and 219

211

 Main article: 211 (number)

212

 Main article: 212 (number)

213

 Main article: 213 (number)

214

 Main article: 214 (number)

215

 Main article: 215 (number)

216

 Main article: 216 (number)

217

 Main article: 217 (number)

218

 Main article: 218 (number)

219

 Main article: 219 (number)