210

210 is a natural number that follows 209 and precedes 211. It is a composite number, as it has divisors other than 1 and itself.

The prime factorization of 210 is 2 × 3 × 5 × 7. This is the product of the first four prime numbers, and for this reason 210 is known as the primorial of 7, usually written as 7#.

Mathematical properties

210 is a triangular number: it is the sum of the integers from 1 to 20, calculated as 20 × 21 ÷ 2 = 210. It is also a simplex number in four dimensions, equal to the number of combinations of 4 items chosen from 10 items: C(10,4) = 210.

Because its prime factorization consists of four distinct primes each appearing once, 210 has 16 divisors in total: 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, and 210. The sum of its proper divisors (those less than 210) exceeds 210, making it an abundant number.

210 is the smallest number divisible by all integers from 1 to 7 except 4. It is also the smallest number that is both the product of the first four primes and ends in zero, making it divisible by 10.

Other uses

Numbers of this kind are used in number theory, particularly in the search for prime numbers, as primorial-based numbers assist in sieving operations. 210 may also appear in other contexts—for example as an area code, a historical date, or a telephone number—but these uses differ from its mathematical meaning.