Number

768

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

Abundant Number Evil Number Pernicious Number Practical Number Recamán's Sequence Semiperfect Number Year

Notable events — 768 AD

Oct 9 Charlemagne becomes king of the Franks.

Events compiled from Wikipedia ↗ · Licensed CC BY-SA 4.0

Historical context — 768 BC

Decade

This article concerns the period 769 BC – 760 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: Monday
January 1, 768
Ended on: Tuesday
December 31, 768
Friday the 13ths: 2
2 Friday the 13ths this year.
Decade: 760s
760–769
Century: 8th century
701–800
Millennium: 1st millennium
1–1000
Years ago: 1,258
1258 years before 2026.

In other calendars

Hebrew: 4528 / 4529 AM
Rosh Hashanah falls in September/October.
Islamic Hijri: 150 / 151 AH
Lunar calendar; year spans differ from Gregorian.
Chinese: Year of the zodiac:Earth zodiac:Monkey
Sexagenary cycle position 45 of 60. Lunar new year falls in late January / mid-February.
Buddhist Era: 1311 BE
Counted from the parinirvana of the Buddha (Theravada / Thai / Sri Lankan convention).
Persian Solar Hijri: 146 / 147 SH
Iranian calendar; Nowruz (new year) falls on the spring equinox.
Ethiopian: 760 / 761 ET
Year boundary at Enkutatash (September 11/12).
Indian National (Saka): 690 / 689 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: 867
Recamán's sequence: a(895) = 768
Square (n²): 589,824
Cube (n³): 452,984,832
Divisor count: 18
σ(n) — sum of divisors: 2,044
φ(n) — Euler's totient: 256
Sum of prime factors: 19

Primality

Prime factorization: 2 ⁸ × 3

Nearest primes: 761 (−7) · 769 (+1)

Divisors & multiples

All divisors (18)

1 · 2 · 3 · 4 · 6 · 8 · 12 · 16 · 24 · 32 · 48 · 64 · 96 · 128 · 192 · 256 · 384 (half) · 768

Aliquot sum (sum of proper divisors): 1,276

Factor pairs (a × b = 768)

1 × 768

2 × 384

3 × 256

4 × 192

6 × 128

8 × 96

12 × 64

16 × 48

24 × 32

First multiples

768 · 1,536 (double) · 2,304 · 3,072 · 3,840 · 4,608 · 5,376 · 6,144 · 6,912 · 7,680

Sums & aliquot sequence

As consecutive integers: 255 + 256 + 257

Aliquot sequence: 768 → 1,276 → 1,244 → 940 → 1,076 → 814 → 554 → 280 → 440 → 640 → 890 → 730 → 602 → 454 → 230 → 202 → 104 — unresolved within range

Representations

In words: seven hundred sixty-eight
Ordinal: 768th
Roman numeral: DCCLXVIII
Binary: 1100000000
Octal: 1400
Hexadecimal: 0x300
Base64: AwA=
One's complement: 64,767 (16-bit)

In other bases

ternary (3) 1001110

quaternary (4) 30000

quinary (5) 11033

senary (6) 3320

septenary (7) 2145

nonary (9) 1043

undecimal (11) 639

duodecimal (12) 540

tridecimal (13) 471

tetradecimal (14) 3cc

pentadecimal (15) 363

Historical numeral systems

Babylonian (base 60): 𒌋𒁹𒁹 𒌋𒌋𒌋𒌋𒁹𒁹𒁹𒁹𒁹𒁹𒁹𒁹
Egyptian hieroglyphic: 𓍢𓍢𓍢𓍢𓍢𓍢𓍢𓎆𓎆𓎆𓎆𓎆𓎆𓏺𓏺𓏺𓏺𓏺𓏺𓏺𓏺
Greek (Milesian): ψξηʹ
Mayan (base 20): 𝋡·𝋲·𝋨
Chinese: 七百六十八
Chinese (financial): 柒佰陸拾捌

In other modern scripts

Eastern Arabic ٧٦٨ Devanagari ७६८ Bengali ৭৬৮ Tamil ௭௬௮ Thai ๗๖๘ Tibetan ༧༦༨ Khmer ៧៦៨ Lao ໗໖໘ Burmese ၇၆၈

Digit at this position in famous constants

π — Pi (π): Digit 768 = 9
e — Euler's number (e): Digit 768 = 0
φ — Golden ratio (φ): Digit 768 = 0
√2 — Pythagoras's (√2): Digit 768 = 1
ln 2 — Natural log of 2: Digit 768 = 5
γ — Euler-Mascheroni (γ): Digit 768 = 4

Also seen as

Goldbach decomposition

Goldbach's conjecture says every even integer greater than 2 is the sum of two primes. For 768, here are decompositions:

7 + 761 = 768
11 + 757 = 768
17 + 751 = 768
29 + 739 = 768
41 + 727 = 768
59 + 709 = 768
67 + 701 = 768
107 + 661 = 768

Showing the first eight; more decompositions exist.

Unicode codepoint

Combining Grave Accent

U+0300

Non-spacing mark (Mn)

UTF-8 encoding: CC 80 (2 bytes).

Lookup U+0300 on Compart ↗ Lookup on FileFormat.Info ↗

Hex color

#000300

RGB(0, 3, 0)

IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.0.3.0.

Address: 0.0.3.0
Class: reserved
IPv4-mapped IPv6: ::ffff:0.0.3.0

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