Number

480

480 is a composite number, even, a calendar year.

480 (four hundred eighty) is an even 3-digit number. It is a composite number with 24 divisors, and factors as 2⁵ × 3 × 5. Its proper divisors sum to 1,032, more than the number itself, making it an abundant number. Written other ways, in Roman numerals it is CDLXXX and in binary, 111100000.

Abundant Number Arithmetic Number Evil Number Gapful Number Harshad / Niven Highly Abundant Practical Number Recamán's Sequence Refactorable Number Semiperfect Number Year

Interestingness

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8 notable facts · grade A

468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492

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Historical context — 480 AD

Calendar year

Year 480 (CDLXXX) was a leap year starting on Tuesday of the Julian calendar.

Excerpt from Wikipedia (en) ↗ · Licensed CC BY-SA 4.0 Read the full article on Wikipedia →

Notable events — 480 BC

Undated The Persian Wars: Greeks lose at Thermopylae and Artemisium but win decisively at Salamis.

Events compiled from Wikipedia ↗ · Licensed CC BY-SA 4.0

Year facts

Year type: Leap year
Divisible by 4 and not by 100; February has 29 days.
Days in year: 366
ISO weeks: 52
Started on: Monday
January 1, 480
Ended on: Tuesday
December 31, 480
Friday the 13ths: 2
2 Friday the 13ths this year.
Decade: 480s
480–489
Century: 5th century
401–500
Millennium: 1st millennium
1–1000
Years ago: 1,546
1546 years before 2026.

In other calendars

Hebrew: 4240 / 4241 AM
Rosh Hashanah falls in September/October.
Chinese: Year of the zodiac:Metal zodiac:Monkey
Sexagenary cycle position 57 of 60. Lunar new year falls in late January / mid-February.
Buddhist Era: 1023 BE
Counted from the parinirvana of the Buddha (Theravada / Thai / Sri Lankan convention).
Ethiopian: 472 / 473 ET
Year boundary at Enkutatash (September 11/12).
Indian National (Saka): 402 / 401 Saka
Indian national calendar; year starts in March.

Properties

Parity: Even
Digit count: 3
Digit sum: 12
Digit product: 0
Digital root: 3
Palindrome: No
Bit width: 9 bits
Reversed: 84
Recamán's sequence: a(360) = 480
Square (n²): 230,400
Cube (n³): 110,592,000
Divisor count: 24
σ(n) — sum of divisors: 1,512
φ(n) — Euler's totient: 128
Sum of prime factors: 18

Primality

Prime factorization: 2 ⁵ × 3 × 5

Nearest primes: 479 (−1) · 487 (+7)

Divisors & multiples

All divisors (24)

1 · 2 · 3 · 4 · 5 · 6 · 8 · 10 · 12 · 15 · 16 · 20 · 24 · 30 · 32 · 40 · 48 · 60 · 80 · 96 · 120 · 160 · 240 (half) · 480

Aliquot sum (sum of proper divisors): 1,032

Factor pairs (a × b = 480)

1 × 480

2 × 240

3 × 160

4 × 120

5 × 96

6 × 80

8 × 60

10 × 48

12 × 40

15 × 32

16 × 30

20 × 24

First multiples

480 · 960 (double) · 1,440 · 1,920 · 2,400 · 2,880 · 3,360 · 3,840 · 4,320 · 4,800

Sums & aliquot sequence

As consecutive integers: 159 + 160 + 161 94 + 95 + 96 + 97 + 98 25 + 26 + … + 39

Aliquot sequence: 480 → 1,032 → 1,608 → 2,472 → 3,768 → 5,712 → 12,144 → 23,568 → 37,440 → 101,244 → 180,996 → 241,356 → 321,836 → 251,044 → 188,290 → 168,830 → 135,082 — unresolved within range

Continued fraction of √n

√480 = [21; (1, 9, 1, 42)]

Period length 4 — the block in parentheses repeats forever.

Representations

In words: four hundred eighty
Ordinal: 480th
Roman numeral: CDLXXX
Binary: 111100000
Octal: 740
Hexadecimal: 0x1E0
Base64: AeA=
One's complement: 65,055 (16-bit)
Scientific notation: 4.8 × 10²
As a duration: 480 s = 8 minutes

In other bases

ternary (3) 122210

quaternary (4) 13200

quinary (5) 3410

senary (6) 2120

septenary (7) 1254

nonary (9) 583

undecimal (11) 3a7

duodecimal (12) 340

tridecimal (13) 2ac

tetradecimal (14) 264

pentadecimal (15) 220

As an angle

480° = 1 × 360° + 120°

120° ≈ 2.094 rad

Compass bearing: ESE (east-southeast)

Why does a circle have 360 degrees? →

Historical numeral systems

Babylonian (base 60): 𒁹𒁹𒁹𒁹𒁹𒁹𒁹𒁹 ·
Egyptian hieroglyphic: 𓍢𓍢𓍢𓍢𓎆𓎆𓎆𓎆𓎆𓎆𓎆𓎆
Greek (Milesian): υπʹ
Mayan (base 20): 𝋡·𝋤·𝋠
Chinese: 四百八十
Chinese (financial): 肆佰捌拾

In other modern scripts

Eastern Arabic ٤٨٠ Devanagari ४८० Bengali ৪৮০ Tamil ௪௮௦ Thai ๔๘๐ Tibetan ༤༨༠ Khmer ៤៨០ Lao ໔໘໐ Burmese ၄၈၀

Digit at this position in famous constants

π — Pi (π): Digit 480 = 2
e — Euler's number (e): Digit 480 = 8
φ — Golden ratio (φ): Digit 480 = 7
√2 — Pythagoras's (√2): Digit 480 = 1
ln 2 — Natural log of 2: Digit 480 = 3
γ — Euler-Mascheroni (γ): Digit 480 = 7

Also seen as

Goldbach decomposition

Goldbach's conjecture says every even integer greater than 2 is the sum of two primes. For 480, here are decompositions:

13 + 467 = 480
17 + 463 = 480
19 + 461 = 480
23 + 457 = 480
31 + 449 = 480
37 + 443 = 480
41 + 439 = 480
47 + 433 = 480

Showing the first eight; more decompositions exist.

Unicode codepoint

Latin Capital Letter A With Dot Above And Macron

U+01E0

Uppercase letter (Lu)

UTF-8 encoding: C7 A0 (2 bytes).

Lookup U+01E0 on Compart ↗ Lookup on FileFormat.Info ↗

Hex color

#0001E0

RGB(0, 1, 224)

IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.0.1.224.

Address: 0.0.1.224
Class: reserved
IPv4-mapped IPv6: ::ffff:0.0.1.224

Unspecified address (0.0.0.0/8) — "this network" placeholder.

NANP area code 480

The number 480 is an active NANP area code (North American Numbering Plan).

Primary area: Eastern suburbs of Phoenix
Region: Arizona
Country: United States

Most NANP area codes have multiple overlays in dense regions; the primary area listed is the historic/largest population center for this code.

Look up area code 480 ↗

Musical pitch

Heard as a frequency, 480 Hz is closest to:

Concert pitch (A4 = 440 Hz): B4 (493.9 Hz, -49¢ — about midway to A♯4)
Scientific pitch (C4 = 256 Hz): B4 (483.3 Hz, -12¢)
Baroque pitch (A4 = 415 Hz): C5 (493.5 Hz, -48¢ — about midway to B4)