Number

680

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

680 (six hundred eighty) is an even 3-digit number. It is a composite number with 16 divisors, and factors as 2³ × 5 × 17. Its proper divisors sum to 940, more than the number itself, making it an abundant number. Written other ways, in Roman numerals it is DCLXXX and in binary, 1010101000.

Abundant Number Evil Number Flippable Happy Number Practical Number Preferred Number Recamán's Sequence Semiperfect Number Tetrahedral Year

Interestingness

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7 notable facts · grade B

668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692

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Historical context — 680 AD

Calendar year

Year 680 (DCLXXX) 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 — 680 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: 53
Long year: contains 53 ISO weeks.
Started on: Thursday
January 1, 680
Ended on: Friday
December 31, 680
Friday the 13ths: 2
2 Friday the 13ths this year.
Decade: 680s
680–689
Century: 7th century
601–700
Millennium: 1st millennium
1–1000
Years ago: 1,346
1346 years before 2026.

In other calendars

Hebrew: 4440 / 4441 AM
Rosh Hashanah falls in September/October.
Islamic Hijri: 60 / 61 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: 1223 BE
Counted from the parinirvana of the Buddha (Theravada / Thai / Sri Lankan convention).
Persian Solar Hijri: 58 / 59 SH
Iranian calendar; Nowruz (new year) falls on the spring equinox.
Ethiopian: 672 / 673 ET
Year boundary at Enkutatash (September 11/12).
Indian National (Saka): 602 / 601 Saka
Indian national calendar; year starts in March.

Properties

Parity: Even
Digit count: 3
Digit sum: 14
Digit product: 0
Digital root: 5
Palindrome: No
Bit width: 10 bits
Reversed: 86
Flips to (rotate 180°): 89
Recamán's sequence: a(2,264) = 680
Square (n²): 462,400
Cube (n³): 314,432,000
Divisor count: 16
σ(n) — sum of divisors: 1,620
φ(n) — Euler's totient: 256
Sum of prime factors: 28

Primality

Prime factorization: 2 ³ × 5 × 17

Nearest primes: 677 (−3) · 683 (+3)

Divisors & multiples

All divisors (16)

1 · 2 · 4 · 5 · 8 · 10 · 17 · 20 · 34 · 40 · 68 · 85 · 136 · 170 · 340 (half) · 680

Aliquot sum (sum of proper divisors): 940

Factor pairs (a × b = 680)

1 × 680

2 × 340

4 × 170

5 × 136

8 × 85

10 × 68

17 × 40

20 × 34

First multiples

680 · 1,360 (double) · 2,040 · 2,720 · 3,400 · 4,080 · 4,760 · 5,440 · 6,120 · 6,800

Sums & aliquot sequence

As a sum of two squares: 2² + 26² = 14² + 22²

As consecutive integers: 134 + 135 + 136 + 137 + 138 35 + 36 + … + 50 32 + 33 + … + 48

Aliquot sequence: 680 → 940 → 1,076 → 814 → 554 → 280 → 440 → 640 → 890 → 730 → 602 → 454 → 230 → 202 → 104 → 106 → 56 — unresolved within range

Continued fraction of √n

√680 = [26; (13, 52)]

Period length 2 — the block in parentheses repeats forever.

Representations

In words: six hundred eighty
Ordinal: 680th
Roman numeral: DCLXXX
Binary: 1010101000
Octal: 1250
Hexadecimal: 0x2A8
Base64: Aqg=
One's complement: 64,855 (16-bit)
Scientific notation: 6.8 × 10²
As a duration: 680 s = 11 minutes, 20 seconds

In other bases

ternary (3) 221012

quaternary (4) 22220

quinary (5) 10210

senary (6) 3052

septenary (7) 1661

nonary (9) 835

undecimal (11) 569

duodecimal (12) 488

tridecimal (13) 404

tetradecimal (14) 368

pentadecimal (15) 305

Palindromic in base 7, base 13

As an angle

680° = 1 × 360° + 320°

320° ≈ 5.585 rad

Compass bearing: NW (northwest)

Why does a circle have 360 degrees? →

Historical numeral systems

Babylonian (base 60): 𒌋𒁹 𒌋𒌋
Egyptian hieroglyphic: 𓍢𓍢𓍢𓍢𓍢𓍢𓎆𓎆𓎆𓎆𓎆𓎆𓎆𓎆
Greek (Milesian): χπʹ
Mayan (base 20): 𝋡·𝋮·𝋠
Chinese: 六百八十
Chinese (financial): 陸佰捌拾

In other modern scripts

Eastern Arabic ٦٨٠ Devanagari ६८० Bengali ৬৮০ Tamil ௬௮௦ Thai ๖๘๐ Tibetan ༦༨༠ Khmer ៦៨០ Lao ໖໘໐ Burmese ၆၈၀

Digit at this position in famous constants

π — Pi (π): Digit 680 = 3
e — Euler's number (e): Digit 680 = 7
φ — Golden ratio (φ): Digit 680 = 9
√2 — Pythagoras's (√2): Digit 680 = 0
ln 2 — Natural log of 2: Digit 680 = 4
γ — Euler-Mascheroni (γ): Digit 680 = 4

Also seen as

Goldbach decomposition

Goldbach's conjecture says every even integer greater than 2 is the sum of two primes. For 680, here are decompositions:

3 + 677 = 680
7 + 673 = 680
19 + 661 = 680
37 + 643 = 680
61 + 619 = 680
67 + 613 = 680
73 + 607 = 680
79 + 601 = 680

Showing the first eight; more decompositions exist.

Unicode codepoint

Latin Small Letter Tc Digraph With Curl

U+02A8

Lowercase letter (Ll)

UTF-8 encoding: CA A8 (2 bytes).

Lookup U+02A8 on Compart ↗ Lookup on FileFormat.Info ↗

Hex color

#0002A8

RGB(0, 2, 168)

IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.0.2.168.

Address: 0.0.2.168
Class: reserved
IPv4-mapped IPv6: ::ffff:0.0.2.168

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

NANP area code 680

The number 680 is an active NANP area code (North American Numbering Plan).

Primary area: Syracuse
Region: New York
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 680 ↗

Musical pitch

Heard as a frequency, 680 Hz is closest to:

Concert pitch (A4 = 440 Hz): F5 (698.5 Hz, -46¢ — about midway to E5)
Scientific pitch (C4 = 256 Hz): F5 (683.4 Hz, -9¢)
Baroque pitch (A4 = 415 Hz): F♯5 (697.9 Hz, -45¢ — about midway to F5)