Number

800

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

800 (eight hundred) is an even 3-digit number. It is a composite number with 18 divisors, and factors as 2⁵ × 5². Its proper divisors sum to 1,153, more than the number itself, making it an abundant number. Written other ways, in Roman numerals it is DCCC and in binary, 1100100000.

Abundant Number Achilles Number Flippable Gapful Number Harshad / Niven Odious Number Pernicious Number Powerful Number Practical Number Recamán's Sequence Semiperfect Number Year

Interestingness

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8 notable facts · grade A

788 789 790 791 792 793 794 795 796 797 798 799 800 801 802 803 804 805 806 807 808 809 810 811 812

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Notable events — 800 AD

Dec 25 Pope Leo III crowns Charlemagne Emperor of the Romans in St. Peter's Basilica.

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

Historical context — 800 BC

Decade

This article concerns the period 809 BC – 800 BC.

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

Year facts

Year type: Leap year
Divisible by 400 (Gregorian leap-year rule exception to the century rule).
Days in year: 366
ISO weeks: 52
Started on: Saturday
January 1, 800
Ended on: Sunday
December 31, 800
Friday the 13ths: 1
One Friday the 13th this year.
Decade: 800s
800–809
Century: 8th century
701–800
Millennium: 1st millennium
1–1000
Years ago: 1,226
1226 years before 2026.

In other calendars

Hebrew: 4560 / 4561 AM
Rosh Hashanah falls in September/October.
Islamic Hijri: 183 / 184 AH
Lunar calendar; year spans differ from Gregorian.
Chinese: Year of the zodiac:Metal zodiac:Dragon
Sexagenary cycle position 17 of 60. Lunar new year falls in late January / mid-February.
Buddhist Era: 1343 BE
Counted from the parinirvana of the Buddha (Theravada / Thai / Sri Lankan convention).
Persian Solar Hijri: 178 / 179 SH
Iranian calendar; Nowruz (new year) falls on the spring equinox.
Ethiopian: 792 / 793 ET
Year boundary at Enkutatash (September 11/12).
Indian National (Saka): 722 / 721 Saka
Indian national calendar; year starts in March.

Properties

Parity: Even
Digit count: 3
Digit sum: 8
Digit product: 0
Digital root: 8
Palindrome: No
Bit width: 10 bits
Reversed: 8
Flips to (rotate 180°): 8
Recamán's sequence: a(291) = 800
Square (n²): 640,000
Cube (n³): 512,000,000
Divisor count: 18
σ(n) — sum of divisors: 1,953
φ(n) — Euler's totient: 320
Sum of prime factors: 20

Primality

Prime factorization: 2 ⁵ × 5 ²

Nearest primes: 797 (−3) · 809 (+9)

Divisors & multiples

All divisors (18)

1 · 2 · 4 · 5 · 8 · 10 · 16 · 20 · 25 · 32 · 40 · 50 · 80 · 100 · 160 · 200 · 400 (half) · 800

Aliquot sum (sum of proper divisors): 1,153

Factor pairs (a × b = 800)

1 × 800

2 × 400

4 × 200

5 × 160

8 × 100

10 × 80

16 × 50

20 × 40

25 × 32

First multiples

800 · 1,600 (double) · 2,400 · 3,200 · 4,000 · 4,800 · 5,600 · 6,400 · 7,200 · 8,000

Sums & aliquot sequence

As a sum of two squares: 4² + 28² = 20² + 20²

As consecutive integers: 158 + 159 + 160 + 161 + 162 20 + 21 + … + 44

Aliquot sequence: 800 → 1,153 → 1 → 0 — terminates at zero

Continued fraction of √n

√800 = [28; (3, 1, 1, 13, 1, 1, 3, 56)]

Period length 8 — the block in parentheses repeats forever.

Representations

In words: eight hundred
Ordinal: 800th
Roman numeral: DCCC
Binary: 1100100000
Octal: 1440
Hexadecimal: 0x320
Base64: AyA=
One's complement: 64,735 (16-bit)
Scientific notation: 8 × 10²
As a duration: 800 s = 13 minutes, 20 seconds

In other bases

ternary (3) 1002122

quaternary (4) 30200

quinary (5) 11200

senary (6) 3412

septenary (7) 2222

nonary (9) 1078

undecimal (11) 668

duodecimal (12) 568

tridecimal (13) 497

tetradecimal (14) 412

pentadecimal (15) 385

Palindromic in base 7

As an angle

800° = 2 × 360° + 80°

80° ≈ 1.396 rad

Compass bearing: E (east)

Why does a circle have 360 degrees? →

Historical numeral systems

Babylonian (base 60): 𒌋𒁹𒁹𒁹 𒌋𒌋
Egyptian hieroglyphic: 𓍢𓍢𓍢𓍢𓍢𓍢𓍢𓍢
Greek (Milesian): ωʹ
Mayan (base 20): 𝋢·𝋠·𝋠
Chinese: 八百
Chinese (financial): 捌佰

In other modern scripts

Eastern Arabic ٨٠٠ Devanagari ८०० Bengali ৮০০ Tamil ௮௦௦ Thai ๘๐๐ Tibetan ༨༠༠ Khmer ៨០០ Lao ໘໐໐ Burmese ၈၀၀

Digit at this position in famous constants

π — Pi (π): Digit 800 = 5
e — Euler's number (e): Digit 800 = 9
φ — Golden ratio (φ): Digit 800 = 7
√2 — Pythagoras's (√2): Digit 800 = 9
ln 2 — Natural log of 2: Digit 800 = 4
γ — Euler-Mascheroni (γ): Digit 800 = 8

Also seen as

Goldbach decomposition

Goldbach's conjecture says every even integer greater than 2 is the sum of two primes. For 800, here are decompositions:

3 + 797 = 800
13 + 787 = 800
31 + 769 = 800
43 + 757 = 800
61 + 739 = 800
67 + 733 = 800
73 + 727 = 800
109 + 691 = 800

Showing the first eight; more decompositions exist.

Unicode codepoint

Combining Minus Sign Below

U+0320

Non-spacing mark (Mn)

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

Lookup U+0320 on Compart ↗ Lookup on FileFormat.Info ↗

Hex color

#000320

RGB(0, 3, 32)

IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.0.3.32.

Address: 0.0.3.32
Class: reserved
IPv4-mapped IPv6: ::ffff:0.0.3.32

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

NANP area code 800

The number 800 is an active NANP area code (North American Numbering Plan).

Primary area: Toll-free
Region: (special)
Country: North America

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 800 ↗

Musical pitch

Heard as a frequency, 800 Hz is closest to:

Concert pitch (A4 = 440 Hz): G5 (784 Hz, +35¢)
Scientific pitch (C4 = 256 Hz): G♯5 (812.7 Hz, -27¢)
Baroque pitch (A4 = 415 Hz): G♯5 (783.4 Hz, +36¢)