Number

306

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

306 (three hundred six) is an even 3-digit number. It is a composite number with 12 divisors, and factors as 2 × 3² × 17. Its proper divisors sum to 396, more than the number itself, making it an abundant number. Written other ways, in Roman numerals it is CCCVI and in binary, 100110010.

Abundant Number Cube-Free Evil Number Harshad / Niven Practical Number Pronic / Oblong Recamán's Sequence Semiperfect Number Year

Interestingness

★ ★ ★ ★ ☆

6 notable facts · grade B

294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318

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Notable events — 306 AD

Jul 25 Constantine is proclaimed emperor at York.

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

Historical context — 306 BC

Calendar year

Year 306 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: Monday
January 1, 306
Ended on: Monday
December 31, 306
Friday the 13ths: 2
2 Friday the 13ths this year.
Decade: 300s
300–309
Century: 4th century
301–400
Millennium: 1st millennium
1–1000
Years ago: 1,720
1720 years before 2026.

In other calendars

Hebrew: 4066 / 4067 AM
Rosh Hashanah falls in September/October.
Chinese: Year of the zodiac:Fire zodiac:Tiger
Sexagenary cycle position 3 of 60. Lunar new year falls in late January / mid-February.
Buddhist Era: 849 BE
Counted from the parinirvana of the Buddha (Theravada / Thai / Sri Lankan convention).
Ethiopian: 298 / 299 ET
Year boundary at Enkutatash (September 11/12).
Indian National (Saka): 228 / 227 Saka
Indian national calendar; year starts in March.

Properties

Parity: Even
Digit count: 3
Digit sum: 9
Digit product: 0
Digital root: 9
Palindrome: No
Bit width: 9 bits
Reversed: 603
Recamán's sequence: a(636) = 306
Square (n²): 93,636
Cube (n³): 28,652,616
Divisor count: 12
σ(n) — sum of divisors: 702
φ(n) — Euler's totient: 96
Sum of prime factors: 25

Primality

Prime factorization: 2 × 3 ² × 17

Nearest primes: 293 (−13) · 307 (+1)

Divisors & multiples

All divisors (12)

1 · 2 · 3 · 6 · 9 · 17 · 18 · 34 · 51 · 102 · 153 (half) · 306

Aliquot sum (sum of proper divisors): 396

Factor pairs (a × b = 306)

1 × 306

2 × 153

3 × 102

6 × 51

9 × 34

17 × 18

First multiples

306 · 612 (double) · 918 · 1,224 · 1,530 · 1,836 · 2,142 · 2,448 · 2,754 · 3,060

Sums & aliquot sequence

As a sum of two squares: 9² + 15²

As consecutive integers: 101 + 102 + 103 75 + 76 + 77 + 78 30 + 31 + … + 38 20 + 21 + … + 31

Aliquot sequence: 306 → 396 → 696 → 1,104 → 1,872 → 3,770 → 3,790 → 3,050 → 2,716 → 2,772 → 5,964 → 10,164 → 19,628 → 19,684 → 22,876 → 26,404 → 30,044 — unresolved within range

Continued fraction of √n

√306 = [17; (2, 34)]

Period length 2 — the block in parentheses repeats forever.

Representations

In words: three hundred six
Ordinal: 306th
Roman numeral: CCCVI
Binary: 100110010
Octal: 462
Hexadecimal: 0x132
Base64: ATI=
One's complement: 65,229 (16-bit)
Scientific notation: 3.06 × 10²
As a duration: 306 s = 5 minutes, 6 seconds

In other bases

ternary (3) 102100

quaternary (4) 10302

quinary (5) 2211

senary (6) 1230

septenary (7) 615

nonary (9) 370

undecimal (11) 259

duodecimal (12) 216

tridecimal (13) 1a7

tetradecimal (14) 17c

pentadecimal (15) 156

As an angle

306°

306° ≈ 5.341 rad

Compass bearing: NW (northwest)

Why does a circle have 360 degrees? →

Historical numeral systems

Babylonian (base 60): 𒁹𒁹𒁹𒁹𒁹 𒁹𒁹𒁹𒁹𒁹𒁹
Egyptian hieroglyphic: 𓍢𓍢𓍢𓏺𓏺𓏺𓏺𓏺𓏺
Greek (Milesian): τϛʹ
Mayan (base 20): 𝋯·𝋦
Chinese: 三百零六
Chinese (financial): 參佰零陸

In other modern scripts

Eastern Arabic ٣٠٦ Devanagari ३०६ Bengali ৩০৬ Tamil ௩௦௬ Thai ๓๐๖ Tibetan ༣༠༦ Khmer ៣០៦ Lao ໓໐໖ Burmese ၃၀၆

Digit at this position in famous constants

π — Pi (π): Digit 306 = 8
e — Euler's number (e): Digit 306 = 0
φ — Golden ratio (φ): Digit 306 = 4
√2 — Pythagoras's (√2): Digit 306 = 5
ln 2 — Natural log of 2: Digit 306 = 8
γ — Euler-Mascheroni (γ): Digit 306 = 7

Also seen as

Goldbach decomposition

Goldbach's conjecture says every even integer greater than 2 is the sum of two primes. For 306, here are decompositions:

13 + 293 = 306
23 + 283 = 306
29 + 277 = 306
37 + 269 = 306
43 + 263 = 306
67 + 239 = 306
73 + 233 = 306
79 + 227 = 306

Showing the first eight; more decompositions exist.

Unicode codepoint

Latin Capital Ligature Ij

U+0132

Uppercase letter (Lu)

UTF-8 encoding: C4 B2 (2 bytes).

Lookup U+0132 on Compart ↗ Lookup on FileFormat.Info ↗

Hex color

#000132

RGB(0, 1, 50)

IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.0.1.50.

Address: 0.0.1.50
Class: reserved
IPv4-mapped IPv6: ::ffff:0.0.1.50

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

NANP area code 306

The number 306 is an active NANP area code (North American Numbering Plan).

Primary area: Statewide
Region: Saskatchewan
Country: Canada

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 306 ↗

Musical pitch

Heard as a frequency, 306 Hz is closest to:

Concert pitch (A4 = 440 Hz): D♯4 (311.1 Hz, -29¢)
Scientific pitch (C4 = 256 Hz): D♯4 (304.4 Hz, +9¢)
Baroque pitch (A4 = 415 Hz): E4 (310.9 Hz, -27¢)

Food additive (E-number)

On an ingredients label, E306 is Tocopherols, an antioxidant or acidity regulator — vitamin E.

E-number reference (Wikipedia) ↗