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Number

684

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

Abundant Number Harshad / Niven Odious Number Pernicious Number Practical Number Recamán's Sequence Semiperfect Number Year

Historical context — 684 AD

Calendar year

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

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Historical context — 684 BC

Decade

This article concerns the period 689 BC – 680 BC.

Excerpt from Wikipedia (en) ↗ · Licensed CC BY-SA 4.0 · English fallback 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

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)
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

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
ʬ
Latin Letter Bilabial Percussive
U+02AC
Lowercase letter (Ll)

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

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.