Number

820

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

820 (eight hundred twenty) is an even 3-digit number. It is a composite number with 12 divisors, and factors as 2² × 5 × 41. Its proper divisors sum to 944, more than the number itself, making it an abundant number. It is the 40th triangular number. Written other ways, in Roman numerals it is DCCCXX and in binary, 1100110100.

Abundant Number Arithmetic Number Cube-Free Descending Digits Happy Number Harshad / Niven Odious Number Pernicious Number Practical Number Preferred Number Recamán's Sequence Semiperfect Number Triangular Year

Interestingness

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10 notable facts · grade A

808 809 810 811 812 813 814 815 816 817 818 819 820 821 822 823 824 825 826 827 828 829 830 831 832

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Historical context — 820 AD

Calendar year

Year 820 (DCCCXX) was a leap year starting on Sunday of the Julian calendar.

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

Historical context — 820 BC

Decade

This article concerns the period 829 BC – 820 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 4 and not by 100; February has 29 days.
Days in year: 366
ISO weeks: 53
Long year: contains 53 ISO weeks.
Started on: Wednesday
January 1, 820
Ended on: Thursday
December 31, 820
Friday the 13ths: 2
2 Friday the 13ths this year.
Decade: 820s
820–829
Century: 9th century
801–900
Millennium: 1st millennium
1–1000
Years ago: 1,206
1206 years before 2026.

In other calendars

Hebrew: 4580 / 4581 AM
Rosh Hashanah falls in September/October.
Islamic Hijri: 204 / 205 AH
Lunar calendar; year spans differ from Gregorian.
Chinese: Year of the zodiac:Metal zodiac:Rat
Sexagenary cycle position 37 of 60. Lunar new year falls in late January / mid-February.
Buddhist Era: 1363 BE
Counted from the parinirvana of the Buddha (Theravada / Thai / Sri Lankan convention).
Persian Solar Hijri: 198 / 199 SH
Iranian calendar; Nowruz (new year) falls on the spring equinox.
Ethiopian: 812 / 813 ET
Year boundary at Enkutatash (September 11/12).
Indian National (Saka): 742 / 741 Saka
Indian national calendar; year starts in March.

Properties

Parity: Even
Digit count: 3
Digit sum: 10
Digit product: 0
Digital root: 1
Palindrome: No
Bit width: 10 bits
Reversed: 28
Recamán's sequence: a(2,108) = 820
Square (n²): 672,400
Cube (n³): 551,368,000
Divisor count: 12
σ(n) — sum of divisors: 1,764
φ(n) — Euler's totient: 320
Sum of prime factors: 50

Primality

Prime factorization: 2 ² × 5 × 41

Nearest primes: 811 (−9) · 821 (+1)

Divisors & multiples

All divisors (12)

1 · 2 · 4 · 5 · 10 · 20 · 41 · 82 · 164 · 205 · 410 (half) · 820

Aliquot sum (sum of proper divisors): 944

Factor pairs (a × b = 820)

1 × 820

2 × 410

4 × 205

5 × 164

10 × 82

20 × 41

First multiples

820 · 1,640 (double) · 2,460 · 3,280 · 4,100 · 4,920 · 5,740 · 6,560 · 7,380 · 8,200

Sums & aliquot sequence

As a sum of two squares: 6² + 28² = 12² + 26²

As consecutive integers: 162 + 163 + 164 + 165 + 166 99 + 100 + … + 106 1 + 2 + … + 40

Aliquot sequence: 820 → 944 → 916 → 694 → 350 → 394 → 200 → 265 → 59 → 1 → 0 — terminates at zero

Continued fraction of √n

√820 = [28; (1, 1, 1, 2, 1, 10, 1, 2, 1, 1, 1, 56)]

Period length 12 — the block in parentheses repeats forever.

Representations

In words: eight hundred twenty
Ordinal: 820th
Roman numeral: DCCCXX
Binary: 1100110100
Octal: 1464
Hexadecimal: 0x334
Base64: AzQ=
One's complement: 64,715 (16-bit)
Scientific notation: 8.2 × 10²
As a duration: 820 s = 13 minutes, 40 seconds

In other bases

ternary (3) 1010101

quaternary (4) 30310

quinary (5) 11240

senary (6) 3444

septenary (7) 2251

nonary (9) 1111

undecimal (11) 686

duodecimal (12) 584

tridecimal (13) 4b1

tetradecimal (14) 428

pentadecimal (15) 39a

Palindromic in base 3, base 9, base 11

As an angle

820° = 2 × 360° + 100°

100° ≈ 1.745 rad

Compass bearing: E (east)

Why does a circle have 360 degrees? →

Historical numeral systems

Babylonian (base 60): 𒌋𒁹𒁹𒁹 𒌋𒌋𒌋𒌋
Egyptian hieroglyphic: 𓍢𓍢𓍢𓍢𓍢𓍢𓍢𓍢𓎆𓎆
Greek (Milesian): ωκʹ
Mayan (base 20): 𝋢·𝋡·𝋠
Chinese: 八百二十
Chinese (financial): 捌佰貳拾

In other modern scripts

Eastern Arabic ٨٢٠ Devanagari ८२० Bengali ৮২০ Tamil ௮௨௦ Thai ๘๒๐ Tibetan ༨༢༠ Khmer ៨២០ Lao ໘໒໐ Burmese ၈၂၀

Digit at this position in famous constants

π — Pi (π): Digit 820 = 2
e — Euler's number (e): Digit 820 = 1
φ — Golden ratio (φ): Digit 820 = 4
√2 — Pythagoras's (√2): Digit 820 = 2
ln 2 — Natural log of 2: Digit 820 = 5
γ — Euler-Mascheroni (γ): Digit 820 = 4

Also seen as

Goldbach decomposition

Goldbach's conjecture says every even integer greater than 2 is the sum of two primes. For 820, here are decompositions:

11 + 809 = 820
23 + 797 = 820
47 + 773 = 820
59 + 761 = 820
101 + 719 = 820
137 + 683 = 820
167 + 653 = 820
173 + 647 = 820

Showing the first eight; more decompositions exist.

Unicode codepoint

Combining Tilde Overlay

U+0334

Non-spacing mark (Mn)

UTF-8 encoding: CC B4 (2 bytes).

Lookup U+0334 on Compart ↗ Lookup on FileFormat.Info ↗

Hex color

#000334

RGB(0, 3, 52)

IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.0.3.52.

Address: 0.0.3.52
Class: reserved
IPv4-mapped IPv6: ::ffff:0.0.3.52

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

Musical pitch

Heard as a frequency, 820 Hz is closest to:

Concert pitch (A4 = 440 Hz): G♯5 (830.6 Hz, -22¢)
Scientific pitch (C4 = 256 Hz): G♯5 (812.7 Hz, +15¢)
Baroque pitch (A4 = 415 Hz): A5 (830 Hz, -21¢)