880 is a natural number that follows 879 and precedes 881. As an integer it appears in arithmetic, measurement, computing and cultural references. Its simple factors and multiple representations make it a useful example in elementary number theory and applied settings such as music and telecommunications.

Mathematical properties

In prime factorization 880 = 2^4 × 5 × 11. It is an even composite number with 20 positive divisors. The sum of all positive divisors is 2,232, so the sum of proper divisors is 1,352, which exceeds 880; therefore 880 is classified as an abundant number. Because 880 is divisible by the sum of its digits (8+8+0 = 16), it is also a Harshad (Niven) number in base 10.

  • All positive divisors: 1, 2, 4, 5, 8, 10, 11, 16, 20, 22, 40, 44, 55, 80, 88, 110, 176, 220, 440, 880.

Representations and notation

Common notations for 880 include Roman numerals DCCCLXXX. In positional bases it is written as 1101110000 in binary, 0x370 in hexadecimal and 1560 in octal. It is divisible by 10 and by 11, and can be expressed as 16 × 55 or 11 × 80, which sometimes simplifies arithmetic in applied problems.

Uses and cultural references

In music, 880 hertz is the standard frequency for the pitch A5, one octave above the concert pitch A4 at 440 Hz; this makes 880 Hz an important reference tone in tuning and acoustics. In telecommunications, +880 is the international country calling code assigned to Bangladesh, used when dialing that country from abroad. Beyond these, 880 commonly appears as a model or product number across industries, though such uses are specific to manufacturers rather than carrying mathematical significance.

The year 880 (AD)

The designation 880 also identifies a year in the Common Era. Year 880 falls in the early medieval period, a time marked by shifting political boundaries in Europe, continued Viking activity in parts of northern Europe, and established dynasties in Asia. References to the year are used in chronology and historical studies to anchor events, documents and developments of that period.

As a compact subject, 880 crosses pure mathematics, practical measurement and cultural domains: it serves as a clear example for factorization and divisor properties, a precise musical frequency, and a memorable international dialing code.