Overview
687 is a positive integer that follows 686 and precedes 688. In arithmetic it is an odd composite number with a simple prime factorization and several elementary properties that situate it among common classes of integers (deficient, non-square, non-cubic).
Mathematical properties
In prime factorization 687 = 3 × 229, where 229 is a prime. Its positive divisors are 1, 3, 229 and 687. The sum of proper divisors is 1 + 3 + 229 = 233, which is less than 687, so 687 is a deficient number. The sum of all divisors (the sigma function) is 920. Euler's totient function φ(687) = (3−1)×(229−1) = 456. Because one of its factors is 3, the decimal digit sum 6 + 8 + 7 = 21 is divisible by 3, providing a quick divisibility check.
Representations and sequences
In binary 687 is written 1010101111, in octal it is 1257 and in hexadecimal it is 0x2AF. It is not a perfect square, cube, triangular, or hexagonal number. In the aliquot sequence (sum of proper divisors iterated) 687 → 233 → 1 → 0, since 233 is prime; thus 687 lies on a short prime-terminated aliquot chain.
Uses, identifiers and distinctions
The three-digit figure appears in ordinary numbering and as an identifier in systems that use short numeric codes. International telephone country code +687 is assigned to New Caledonia. Mathematically 687 is a simple composite with just two prime factors, distinguishing it from prime or highly composite integers.
Year designations
The numerals 687 also label years in the Gregorian/Julian scheme: AD 687 and 687 BC. One well-known event dated to AD 687 is the Battle of Tertry in Frankish lands, where Pepin of Herstal secured a decisive victory that affected the balance of power among the Frankish realms.