Overview

480 is a positive integer that sits between 479 and 481. It is a composite number with widespread practical appearances—from units of time to video resolutions and industrial electrical systems. As a moderately large even number, 480's structure of prime factors gives it many divisors and makes it useful in applications that require divisible quantities.

Mathematical properties

In prime factorization 480 = 2^5 × 3 × 5. That factorization yields 24 positive divisors. Some common arithmetic characteristics and representations include:

  • Divisors: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 80, 96, 120, 160, 240, 480.
  • Sum of divisors σ(480) = 1512; sum of proper divisors = 1032, so 480 is abundant (proper divisors sum exceeds the number).
  • Euler's totient φ(480) = 128, giving the count of integers up to 480 that are coprime with it.
  • Common representations: binary 111100000, hexadecimal 0x1E0, octal 0740, Roman numeral CDLXXX.

Uses and occurrences

480 appears in many technical and everyday contexts because of its divisibility and roundness in multiple bases.

  • Time: 480 seconds equals 8 minutes, a convenient chunk for scheduling and timing.
  • Video and display: 480i and 480p denote standard-definition vertical resolutions (480 scan lines); the VGA mode 640×480 is a historically important display format.
  • Electric power: 480 volts (typically three-phase) is a common industrial distribution voltage in North America for motor and heavy-equipment supply.
  • Music technology: many digital audio and MIDI systems use 480 pulses per quarter note (PPQ) as a timing resolution in sequencers.

Historical years and cultural notes

The numeral 480 also identifies calendar years. In 480 BC, notable events in the Greco-Persian Wars—such as the battles of Thermopylae and Salamis—occurred. The year 480 AD falls in Late Antiquity and is referenced in chronologies of the waning Western Roman Empire and early medieval Europe. Using the number as a label for years highlights how integers serve both mathematical and historical indexing purposes.

Notable distinctions

Because 480 combines a high power of two with the primes 3 and 5, it is highly factorable and practical for partitioning tasks (scheduling, dividing materials, or arranging digital timing). It is not a prime, perfect, or square number, but its structure makes it a useful reference value across engineering, computing and everyday measurement.