Number

684

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

684 (six hundred eighty-four) is an even 3-digit number. It is a composite number with 18 divisors, and factors as 2² × 3² × 19. Its proper divisors sum to 1,136, more than the number itself, making it an abundant number. Written other ways, in Roman numerals it is DCLXXXIV and in binary, 1010101100.

Abundant Number Cube-Free Harshad / Niven Odious Number Pernicious Number Practical Number Recamán's Sequence Refactorable Number Semiperfect Number Year

Interestingness

★ ★ ★ ★ ☆

6 notable facts · grade B

672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696

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Historical context — 684 AD

Calendar year

Year 684 (DCLXXXIV) was a leap year starting on Friday of the Julian calendar.

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

Historical context — 684 BC

Decade

This article concerns the period 689 BC – 680 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, 684
Ended on: Wednesday
December 31, 684
Friday the 13ths: 1
One Friday the 13th this year.
Decade: 680s
680–689
Century: 7th century
601–700
Millennium: 1st millennium
1–1000
Years ago: 1,342
1342 years before 2026.

In other calendars

Hebrew: 4444 / 4445 AM
Rosh Hashanah falls in September/October.
Islamic Hijri: 64 / 65 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: 1227 BE
Counted from the parinirvana of the Buddha (Theravada / Thai / Sri Lankan convention).
Persian Solar Hijri: 62 / 63 SH
Iranian calendar; Nowruz (new year) falls on the spring equinox.
Ethiopian: 676 / 677 ET
Year boundary at Enkutatash (September 11/12).
Indian National (Saka): 606 / 605 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: 486
Recamán's sequence: a(2,256) = 684
Square (n²): 467,856
Cube (n³): 320,013,504
Divisor count: 18
σ(n) — sum of divisors: 1,820
φ(n) — Euler's totient: 216
Sum of prime factors: 29

Primality

Prime factorization: 2 ² × 3 ² × 19

Nearest primes: 683 (−1) · 691 (+7)

Divisors & multiples

All divisors (18)

1 · 2 · 3 · 4 · 6 · 9 · 12 · 18 · 19 · 36 · 38 · 57 · 76 · 114 · 171 · 228 · 342 (half) · 684

Aliquot sum (sum of proper divisors): 1,136

Factor pairs (a × b = 684)

1 × 684

2 × 342

3 × 228

4 × 171

6 × 114

9 × 76

12 × 57

18 × 38

19 × 36

First multiples

684 · 1,368 (double) · 2,052 · 2,736 · 3,420 · 4,104 · 4,788 · 5,472 · 6,156 · 6,840

Sums & aliquot sequence

As consecutive integers: 227 + 228 + 229 82 + 83 + … + 89 72 + 73 + … + 80 27 + 28 + … + 45

Aliquot sequence: 684 → 1,136 → 1,096 → 974 → 490 → 536 → 484 → 447 → 153 → 81 → 40 → 50 → 43 → 1 → 0 — terminates at zero

Continued fraction of √n

√684 = [26; (6, 1, 1, 12, 1, 1, 6, 52)]

Period length 8 — the block in parentheses repeats forever.

Representations

In words: six hundred eighty-four
Ordinal: 684th
Roman numeral: DCLXXXIV
Binary: 1010101100
Octal: 1254
Hexadecimal: 0x2AC
Base64: Aqw=
One's complement: 64,851 (16-bit)
Scientific notation: 6.84 × 10²
As a duration: 684 s = 11 minutes, 24 seconds

In other bases

ternary (3) 221100

quaternary (4) 22230

quinary (5) 10214

senary (6) 3100

septenary (7) 1665

nonary (9) 840

undecimal (11) 572

duodecimal (12) 490

tridecimal (13) 408

tetradecimal (14) 36c

pentadecimal (15) 309

As an angle

684° = 1 × 360° + 324°

324° ≈ 5.655 rad

Compass bearing: NW (northwest)

Why does a circle have 360 degrees? →

Historical numeral systems

Babylonian (base 60): 𒌋𒁹 𒌋𒌋𒁹𒁹𒁹𒁹
Egyptian hieroglyphic: 𓍢𓍢𓍢𓍢𓍢𓍢𓎆𓎆𓎆𓎆𓎆𓎆𓎆𓎆𓏺𓏺𓏺𓏺
Greek (Milesian): χπδʹ
Mayan (base 20): 𝋡·𝋮·𝋤
Chinese: 六百八十四
Chinese (financial): 陸佰捌拾肆

In other modern scripts

Eastern Arabic ٦٨٤ Devanagari ६८४ Bengali ৬৮৪ Tamil ௬௮௪ Thai ๖๘๔ Tibetan ༦༨༤ Khmer ៦៨៤ Lao ໖໘໔ Burmese ၆၈၄

Digit at this position in famous constants

π — Pi (π): Digit 684 = 5
e — Euler's number (e): Digit 684 = 1
φ — Golden ratio (φ): Digit 684 = 6
√2 — Pythagoras's (√2): Digit 684 = 8
ln 2 — Natural log of 2: Digit 684 = 7
γ — Euler-Mascheroni (γ): Digit 684 = 4

Also seen as

Goldbach decomposition

Goldbach's conjecture says every even integer greater than 2 is the sum of two primes. For 684, here are decompositions:

7 + 677 = 684
11 + 673 = 684
23 + 661 = 684
31 + 653 = 684
37 + 647 = 684
41 + 643 = 684
43 + 641 = 684
53 + 631 = 684

Showing the first eight; more decompositions exist.

Unicode codepoint

Latin Letter Bilabial Percussive

U+02AC

Lowercase letter (Ll)

UTF-8 encoding: CA AC (2 bytes).

Lookup U+02AC on Compart ↗ Lookup on FileFormat.Info ↗

Hex color

#0002AC

RGB(0, 2, 172)

IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.0.2.172.

Address: 0.0.2.172
Class: reserved
IPv4-mapped IPv6: ::ffff:0.0.2.172

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

NANP area code 684

The number 684 is an active NANP area code (North American Numbering Plan).

Primary area: Statewide
Region: American Samoa
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 684 ↗

Musical pitch

Heard as a frequency, 684 Hz is closest to:

Concert pitch (A4 = 440 Hz): F5 (698.5 Hz, -36¢)
Scientific pitch (C4 = 256 Hz): F5 (683.4 Hz, +1¢)
Baroque pitch (A4 = 415 Hz): F♯5 (697.9 Hz, -35¢)