840

840 is the natural number that follows 839 and precedes 841. In mathematics, it is an even composite number whose prime factorization is 2^3 × 3 × 5 × 7.

It has 32 positive divisors, which makes it a highly composite number. It is the least common multiple of the integers 1 through 8. In base 10 it is a Harshad number, since 8+4+0 = 12 and 840 is divisible by 12.

Representations include Roman numerals DCCCXL; in binary it is 1101001000; and in hexadecimal it is 0x348.

As a year in the Anno Domini era, 840 AD was a leap year in the Julian calendar. The year saw the death of Louis the Pious, whose passing led to succession disputes among his heirs and set the stage for the Carolingian fragmentation culminating in the Treaty of Verdun in 843.

840 also appears in calendrical and numerical contexts as the product of small primes and the LCM of 1–8, giving it a role in number theory and modular arithmetic discussions.