1370 is both a natural number and a year designation in the Common Era. As an integer it lies between 1369 and 1371. As a year label it belongs to the 14th century and is usually placed within the Late Middle Ages when the Julian calendar was in widespread use in Europe.

Mathematical properties

Arithmetically, 1370 is an even composite integer. Its prime factorization is 2 × 5 × 137, where 137 is prime. Because it is the product of three distinct primes it is squarefree and has 8 positive divisors: 1, 2, 5, 10, 137, 274, 685 and 1370. The sum of all divisors (σ) is 2,484, so the sum of proper divisors is 1,114; this makes 1370 a deficient number (the proper divisors sum to less than the number itself).

  • Number of divisors: 8
  • Sum of divisors (σ): 2,484; sum of proper divisors: 1,114
  • Euler totient φ(1370): 544
  • Möbius function μ(1370): −1 (product of three distinct primes)
  • Decimal digits: ends with 0 (divisible by 10); digit sum 1+3+7+0 = 11
  • Binary: 10101011010; hexadecimal: 0x55A; Roman numerals: MCCCLXX

Notation and practical representation

Because 1370 = 10 × 137, many calculations involving the number reduce to calculations with 137 followed by a decimal shift. Its factorization into small primes (2 and 5) together with a larger prime (137) makes it a convenient example in elementary number theory when illustrating divisor functions, Euler's totient, and the Möbius function.

The year 1370 in broad context

The year 1370 CE sits within a period of political fragmentation and cultural change across much of Eurasia and parts of Africa. In Europe the long-term effects of mid-14th-century plague outbreaks and intermittent warfare continued to shape societies and economies; conflicts such as the Hundred Years' War affected regional politics and military developments. In East Asia the Ming dynasty had recently replaced the Yuan dynasty in China (1368), prompting administrative and cultural shifts. In Central Asia and the Middle East, successor states and regional powers continued to emerge from the political rearrangements that followed the earlier Mongol expansions.

Away from Eurasia, various complex societies and states existed in the Americas and sub-Saharan Africa, each following their own trajectories. Precise events and dates for 1370 vary by region and source, so summaries here emphasize context rather than disputed specifics.

Uses and cultural notes

As a round multiple of ten and a relatively small composite number, 1370 commonly appears in practical lists such as model numbers, catalog identifiers, and financial figures. In education and exposition it is used to illustrate factorization, divisor sums, and basic multiplicative arithmetic because its factors combine very small primes with a larger prime factor. Considered as a year, 1370 is useful for discussing broad historical trends of the late 14th century without centring any single, contested event.