Number

678

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

678 (six hundred seventy-eight) is an even 3-digit number. It is a composite number with 8 divisors, and factors as 2 × 3 × 113. Its proper divisors sum to 690, more than the number itself, making it an abundant number. Written other ways, in Roman numerals it is DCLXXVIII and in binary, 1010100110.

Abundant Number Arithmetic Number Ascending Digits Consecutive Digits Cube-Free Odious Number Pernicious Number Recamán's Sequence Semiperfect Number Sphenic Number Squarefree Year

Interestingness

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8 notable facts · grade A

666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690

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Historical context — 678 AD

Calendar year

Year 678 (DCLXXVIII) was a common 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 — 678 BC

Calendar year

The year 678 BC was a year of the pre-Julian Roman calendar.

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

Year facts

Year type: Common year
Standard 365-day year; not divisible by 4 (or divisible by 100 but not 400).
Days in year: 365
ISO weeks: 52
Started on: Tuesday
January 1, 678
Ended on: Tuesday
December 31, 678
Friday the 13ths: 2
2 Friday the 13ths this year.
Decade: 670s
670–679
Century: 7th century
601–700
Millennium: 1st millennium
1–1000
Years ago: 1,348
1348 years before 2026.

In other calendars

Hebrew: 4438 / 4439 AM
Rosh Hashanah falls in September/October.
Islamic Hijri: 58 / 59 AH
Lunar calendar; year spans differ from Gregorian.
Chinese: Year of the zodiac:Earth zodiac:Tiger
Sexagenary cycle position 15 of 60. Lunar new year falls in late January / mid-February.
Buddhist Era: 1221 BE
Counted from the parinirvana of the Buddha (Theravada / Thai / Sri Lankan convention).
Persian Solar Hijri: 56 / 57 SH
Iranian calendar; Nowruz (new year) falls on the spring equinox.
Ethiopian: 670 / 671 ET
Year boundary at Enkutatash (September 11/12).
Indian National (Saka): 600 / 599 Saka
Indian national calendar; year starts in March.

Properties

Parity: Even
Digit count: 3
Digit sum: 21
Digit product: 336
Digital root: 3
Palindrome: No
Bit width: 10 bits
Reversed: 876
Recamán's sequence: a(2,268) = 678
Square (n²): 459,684
Cube (n³): 311,665,752
Divisor count: 8
σ(n) — sum of divisors: 1,368
φ(n) — Euler's totient: 224
Sum of prime factors: 118

Primality

Prime factorization: 2 × 3 × 113

Nearest primes: 677 (−1) · 683 (+5)

Divisors & multiples

All divisors (8)

1 · 2 · 3 · 6 · 113 · 226 · 339 (half) · 678

Aliquot sum (sum of proper divisors): 690

Factor pairs (a × b = 678)

1 × 678

2 × 339

3 × 226

6 × 113

First multiples

678 · 1,356 (double) · 2,034 · 2,712 · 3,390 · 4,068 · 4,746 · 5,424 · 6,102 · 6,780

Sums & aliquot sequence

As consecutive integers: 225 + 226 + 227 168 + 169 + 170 + 171 51 + 52 + … + 62

Aliquot sequence: 678 → 690 → 1,038 → 1,050 → 1,926 → 2,286 → 2,706 → 3,342 → 3,354 → 4,038 → 4,050 → 7,203 → 4,001 → 1 → 0 — terminates at zero

Continued fraction of √n

√678 = [26; (26, 52)]

Period length 2 — the block in parentheses repeats forever.

Representations

In words: six hundred seventy-eight
Ordinal: 678th
Roman numeral: DCLXXVIII
Binary: 1010100110
Octal: 1246
Hexadecimal: 0x2A6
Base64: AqY=
One's complement: 64,857 (16-bit)
Scientific notation: 6.78 × 10²
As a duration: 678 s = 11 minutes, 18 seconds

In other bases

ternary (3) 221010

quaternary (4) 22212

quinary (5) 10203

senary (6) 3050

septenary (7) 1656

nonary (9) 833

undecimal (11) 567

duodecimal (12) 486

tridecimal (13) 402

tetradecimal (14) 366

pentadecimal (15) 303

Palindromic in base 15

As an angle

678° = 1 × 360° + 318°

318° ≈ 5.55 rad

Compass bearing: NW (northwest)

Why does a circle have 360 degrees? →

Historical numeral systems

Babylonian (base 60): 𒌋𒁹 𒌋𒁹𒁹𒁹𒁹𒁹𒁹𒁹𒁹
Egyptian hieroglyphic: 𓍢𓍢𓍢𓍢𓍢𓍢𓎆𓎆𓎆𓎆𓎆𓎆𓎆𓏺𓏺𓏺𓏺𓏺𓏺𓏺𓏺
Greek (Milesian): χοηʹ
Mayan (base 20): 𝋡·𝋭·𝋲
Chinese: 六百七十八
Chinese (financial): 陸佰柒拾捌

In other modern scripts

Eastern Arabic ٦٧٨ Devanagari ६७८ Bengali ৬৭৮ Tamil ௬௭௮ Thai ๖๗๘ Tibetan ༦༧༨ Khmer ៦៧៨ Lao ໖໗໘ Burmese ၆၇၈

Digit at this position in famous constants

π — Pi (π): Digit 678 = 8
e — Euler's number (e): Digit 678 = 0
φ — Golden ratio (φ): Digit 678 = 5
√2 — Pythagoras's (√2): Digit 678 = 1
ln 2 — Natural log of 2: Digit 678 = 7
γ — Euler-Mascheroni (γ): Digit 678 = 8

Also seen as

Goldbach decomposition

Goldbach's conjecture says every even integer greater than 2 is the sum of two primes. For 678, here are decompositions:

5 + 673 = 678
17 + 661 = 678
19 + 659 = 678
31 + 647 = 678
37 + 641 = 678
47 + 631 = 678
59 + 619 = 678
61 + 617 = 678

Showing the first eight; more decompositions exist.

Unicode codepoint

Latin Small Letter Ts Digraph

U+02A6

Lowercase letter (Ll)

UTF-8 encoding: CA A6 (2 bytes).

Lookup U+02A6 on Compart ↗ Lookup on FileFormat.Info ↗

Hex color

#0002A6

RGB(0, 2, 166)

IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.0.2.166.

Address: 0.0.2.166
Class: reserved
IPv4-mapped IPv6: ::ffff:0.0.2.166

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

NANP area code 678

The number 678 is an active NANP area code (North American Numbering Plan).

Primary area: Atlanta
Region: Georgia
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 678 ↗

Musical pitch

Heard as a frequency, 678 Hz is closest to:

Concert pitch (A4 = 440 Hz): E5 (659.3 Hz, +49¢ — about midway to F5)
Scientific pitch (C4 = 256 Hz): F5 (683.4 Hz, -14¢)
Baroque pitch (A4 = 415 Hz): F5 (658.8 Hz, +50¢ — about midway to F♯5)