1288: the number and the year

Overview of 1288 as an integer and as the calendar year: mathematical facts (factorization, divisors, representations) and major historical events such as the Battles of Worringen and Bạch Đằng and the election of Nicholas IV.

1288 can denote either the integer after 1287 or the calendar year AD 1288. As a number it appears in elementary number theory and in computing representations; as a year it is associated with several decisive medieval events in Europe and East Asia that affected regional power and independence.

Numeric properties

Mathematically, 1288 is an even composite integer. Its prime factorization is 2^3 × 7 × 23, so it is 8 × 161. It has 16 positive divisors and the sum of all divisors equals 2880; the sum of proper divisors is therefore 1592, which exceeds 1288, making it an abundant number. The Euler totient φ(1288) equals 528. In common numeral systems it is written MCCLXXXVIII in Roman numerals, 10100001000 in binary, 0x508 in hexadecimal and 2410 in octal.

Year 1288: Europe and the papacy

In Europe the year 1288 saw conflicts among regional rulers in the High Middle Ages. One prominent engagement attributed to this year is the Battle of Worringen in the Lower Rhine, a large-scale encounter whose outcome altered local lordship, increased the autonomy of some towns and affected control of the Duchy of Limburg. In the same year a new pope, Nicholas IV, was chosen; he is remembered as the first Franciscan to hold the papacy and led the church in a period of continuing political disputes among European powers.

Year 1288: East and Southeast Asia

In East and Southeast Asia, 1288 is notable for a decisive victory by Đại Việt forces over a Mongol-led invasion. Local commanders employed river and coastal tactics, including the use of prepared obstacles and timing with tides, to damage the invading fleet and force its withdrawal. That campaign marked a key moment in resisting Mongol attempts to impose direct control over the region.

Context and significance

Whether treated as an integer or as a historical year, 1288 connects routine arithmetical properties with moments of political change. Its arithmetic features are of ordinary interest in divisor theory and digital representation; the events of AD 1288 illustrate shifting balances of power in medieval Europe and the resilience of independent states in East Asia in the face of larger empires.

Notable distinctions

Mathematical: composite and abundant, with prime factors 2^3·7·23 and φ(1288)=528.
Historical (Europe): year of the Battle of Worringen and the election of Nicholas IV (the first Franciscan pope).
Historical (Asia): year of a major Đại Việt victory that helped repel a Mongol expedition.