Number

864

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

864 (eight hundred sixty-four) is an even 3-digit number. It is a composite number with 24 divisors, and factors as 2⁵ × 3³. Its proper divisors sum to 1,656, more than the number itself, making it an abundant number. Written other ways, in Roman numerals it is DCCCLXIV and in binary, 1101100000.

Abundant Number Achilles Number Arithmetic Number Descending Digits Evil Number Harshad / Niven Powerful Number Practical Number Recamán's Sequence Refactorable Number Semiperfect Number Stepped Digits Year

Interestingness

★ ★ ★ ★ ★

10 notable facts · grade A

852 853 854 855 856 857 858 859 860 861 862 863 864 865 866 867 868 869 870 871 872 873 874 875 876

less more

Historical context — 864 AD

Calendar year

Year 864 (DCCCLXIV) was a leap year starting on Saturday of the Julian calendar.

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

Historical context — 864 BC

Decade

This article concerns the period 869 BC – 860 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: 52
Started on: Tuesday
January 1, 864
Ended on: Wednesday
December 31, 864
Friday the 13ths: 1
One Friday the 13th this year.
Decade: 860s
860–869
Century: 9th century
801–900
Millennium: 1st millennium
1–1000
Years ago: 1,162
1162 years before 2026.

In other calendars

Hebrew: 4624 / 4625 AM
Rosh Hashanah falls in September/October.
Islamic Hijri: 249 / 250 AH
Lunar calendar; year spans differ from Gregorian.
Chinese: Year of the zodiac:Wood zodiac:Monkey
Sexagenary cycle position 21 of 60. Lunar new year falls in late January / mid-February.
Buddhist Era: 1407 BE
Counted from the parinirvana of the Buddha (Theravada / Thai / Sri Lankan convention).
Persian Solar Hijri: 242 / 243 SH
Iranian calendar; Nowruz (new year) falls on the spring equinox.
Ethiopian: 856 / 857 ET
Year boundary at Enkutatash (September 11/12).
Indian National (Saka): 786 / 785 Saka
Indian national calendar; year starts in March.

Properties

Parity: Even
Digit count: 3
Digit sum: 18
Digit product: 192
Digital root: 9
Palindrome: No
Bit width: 10 bits
Reversed: 468
Recamán's sequence: a(803) = 864
Square (n²): 746,496
Cube (n³): 644,972,544
Divisor count: 24
σ(n) — sum of divisors: 2,520
φ(n) — Euler's totient: 288
Sum of prime factors: 19

Primality

Prime factorization: 2 ⁵ × 3 ³

Nearest primes: 863 (−1) · 877 (+13)

Divisors & multiples

All divisors (24)

1 · 2 · 3 · 4 · 6 · 8 · 9 · 12 · 16 · 18 · 24 · 27 · 32 · 36 · 48 · 54 · 72 · 96 · 108 · 144 · 216 · 288 · 432 (half) · 864

Aliquot sum (sum of proper divisors): 1,656

Factor pairs (a × b = 864)

1 × 864

2 × 432

3 × 288

4 × 216

6 × 144

8 × 108

9 × 96

12 × 72

16 × 54

18 × 48

24 × 36

27 × 32

First multiples

864 · 1,728 (double) · 2,592 · 3,456 · 4,320 · 5,184 · 6,048 · 6,912 · 7,776 · 8,640

Sums & aliquot sequence

As consecutive integers: 287 + 288 + 289 92 + 93 + … + 100 19 + 20 + … + 45

Aliquot sequence: 864 → 1,656 → 3,024 → 6,896 → 6,496 → 8,624 → 12,580 → 16,148 → 14,764 → 11,080 → 13,940 → 17,812 → 14,304 → 23,496 → 41,304 → 62,016 → 120,864 — unresolved within range

Continued fraction of √n

√864 = [29; (2, 1, 1, 5, 1, 13, 1, 5, 1, 1, 2, 58)]

Period length 12 — the block in parentheses repeats forever.

Representations

In words: eight hundred sixty-four
Ordinal: 864th
Roman numeral: DCCCLXIV
Binary: 1101100000
Octal: 1540
Hexadecimal: 0x360
Base64: A2A=
One's complement: 64,671 (16-bit)
Scientific notation: 8.64 × 10²
As a duration: 864 s = 14 minutes, 24 seconds

In other bases

ternary (3) 1012000

quaternary (4) 31200

quinary (5) 11424

senary (6) 4000

septenary (7) 2343

nonary (9) 1160

undecimal (11) 716

duodecimal (12) 600

tridecimal (13) 516

tetradecimal (14) 45a

pentadecimal (15) 3c9

As an angle

864° = 2 × 360° + 144°

144° ≈ 2.513 rad

Compass bearing: SE (southeast)

Why does a circle have 360 degrees? →

Historical numeral systems

Babylonian (base 60): 𒌋𒁹𒁹𒁹𒁹 𒌋𒌋𒁹𒁹𒁹𒁹
Egyptian hieroglyphic: 𓍢𓍢𓍢𓍢𓍢𓍢𓍢𓍢𓎆𓎆𓎆𓎆𓎆𓎆𓏺𓏺𓏺𓏺
Greek (Milesian): ωξδʹ
Mayan (base 20): 𝋢·𝋣·𝋤
Chinese: 八百六十四
Chinese (financial): 捌佰陸拾肆

In other modern scripts

Eastern Arabic ٨٦٤ Devanagari ८६४ Bengali ৮৬৪ Tamil ௮௬௪ Thai ๘๖๔ Tibetan ༨༦༤ Khmer ៨៦៤ Lao ໘໖໔ Burmese ၈၆၄

Digit at this position in famous constants

π — Pi (π): Digit 864 = 3
e — Euler's number (e): Digit 864 = 3
φ — Golden ratio (φ): Digit 864 = 0
√2 — Pythagoras's (√2): Digit 864 = 4
ln 2 — Natural log of 2: Digit 864 = 4
γ — Euler-Mascheroni (γ): Digit 864 = 6

Also seen as

Goldbach decomposition

Goldbach's conjecture says every even integer greater than 2 is the sum of two primes. For 864, here are decompositions:

5 + 859 = 864
7 + 857 = 864
11 + 853 = 864
37 + 827 = 864
41 + 823 = 864
43 + 821 = 864
53 + 811 = 864
67 + 797 = 864

Showing the first eight; more decompositions exist.

Unicode codepoint

Combining Double Tilde

U+0360

Non-spacing mark (Mn)

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

Lookup U+0360 on Compart ↗ Lookup on FileFormat.Info ↗

Hex color

#000360

RGB(0, 3, 96)

IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.0.3.96.

Address: 0.0.3.96
Class: reserved
IPv4-mapped IPv6: ::ffff:0.0.3.96

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

NANP area code 864

The number 864 is an active NANP area code (North American Numbering Plan).

Primary area: Greenville / Spartanburg
Region: South Carolina
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 864 ↗

Musical pitch

Heard as a frequency, 864 Hz is closest to:

Concert pitch (A4 = 440 Hz): A5 (880 Hz, -32¢)
Scientific pitch (C4 = 256 Hz): A5 (861.1 Hz, +6¢)
Baroque pitch (A4 = 415 Hz): A♯5 (879.4 Hz, -30¢)