Number

406

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

406 (four hundred six) is an even 3-digit number. It is a composite number with 8 divisors, and factors as 2 × 7 × 29. It is the 28th triangular number. Written other ways, in Roman numerals it is CDVI and in binary, 110010110.

Arithmetic Number Cube-Free Deficient Number Odious Number Pernicious Number Recamán's Sequence Sphenic Number Squarefree Triangular Year

Interestingness

★ ★ ★ ★ ☆

6 notable facts · grade B

394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418

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Historical context — 406 AD

Calendar year

Year 406 (CDVI) was a common year starting on Monday of the Julian calendar.

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

Historical context — 406 BC

Calendar year

Year 406 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: Sunday
January 1, 406
Ended on: Sunday
December 31, 406
Friday the 13ths: 2
2 Friday the 13ths this year.
Decade: 400s
400–409
Century: 5th century
401–500
Millennium: 1st millennium
1–1000
Years ago: 1,620
1620 years before 2026.

In other calendars

Hebrew: 4166 / 4167 AM
Rosh Hashanah falls in September/October.
Chinese: Year of the zodiac:Fire zodiac:Horse
Sexagenary cycle position 43 of 60. Lunar new year falls in late January / mid-February.
Buddhist Era: 949 BE
Counted from the parinirvana of the Buddha (Theravada / Thai / Sri Lankan convention).
Ethiopian: 398 / 399 ET
Year boundary at Enkutatash (September 11/12).
Indian National (Saka): 328 / 327 Saka
Indian national calendar; year starts in March.

Properties

Parity: Even
Digit count: 3
Digit sum: 10
Digit product: 0
Digital root: 1
Palindrome: No
Bit width: 9 bits
Reversed: 604
Recamán's sequence: a(504) = 406
Square (n²): 164,836
Cube (n³): 66,923,416
Divisor count: 8
σ(n) — sum of divisors: 720
φ(n) — Euler's totient: 168
Sum of prime factors: 38

Primality

Prime factorization: 2 × 7 × 29

Nearest primes: 401 (−5) · 409 (+3)

Divisors & multiples

All divisors (8)

1 · 2 · 7 · 14 · 29 · 58 · 203 (half) · 406

Aliquot sum (sum of proper divisors): 314

Factor pairs (a × b = 406)

1 × 406

2 × 203

7 × 58

14 × 29

First multiples

406 · 812 (double) · 1,218 · 1,624 · 2,030 · 2,436 · 2,842 · 3,248 · 3,654 · 4,060

Sums & aliquot sequence

As consecutive integers: 100 + 101 + 102 + 103 55 + 56 + … + 61 1 + 2 + … + 28

Aliquot sequence: 406 → 314 → 160 → 218 → 112 → 136 → 134 → 70 → 74 → 40 → 50 → 43 → 1 → 0 — terminates at zero

Continued fraction of √n

√406 = [20; (6, 1, 2, 4, 7, 1, 4, 1, 7, 4, 2, 1, 6, 40)]

Period length 14 — the block in parentheses repeats forever.

Representations

In words: four hundred six
Ordinal: 406th
Roman numeral: CDVI
Binary: 110010110
Octal: 626
Hexadecimal: 0x196
Base64: AZY=
One's complement: 65,129 (16-bit)
Scientific notation: 4.06 × 10²
As a duration: 406 s = 6 minutes, 46 seconds

In other bases

ternary (3) 120001

quaternary (4) 12112

quinary (5) 3111

senary (6) 1514

septenary (7) 1120

nonary (9) 501

undecimal (11) 33a

duodecimal (12) 29a

tridecimal (13) 253

tetradecimal (14) 210

pentadecimal (15) 1c1

Palindromic in base 8, base 15

As an angle

406° = 1 × 360° + 46°

46° ≈ 0.803 rad

Compass bearing: NE (northeast)

Why does a circle have 360 degrees? →

Historical numeral systems

Babylonian (base 60): 𒁹𒁹𒁹𒁹𒁹𒁹 𒌋𒌋𒌋𒌋𒁹𒁹𒁹𒁹𒁹𒁹
Egyptian hieroglyphic: 𓍢𓍢𓍢𓍢𓏺𓏺𓏺𓏺𓏺𓏺
Greek (Milesian): υϛʹ
Mayan (base 20): 𝋡·𝋠·𝋦
Chinese: 四百零六
Chinese (financial): 肆佰零陸

In other modern scripts

Eastern Arabic ٤٠٦ Devanagari ४०६ Bengali ৪০৬ Tamil ௪௦௬ Thai ๔๐๖ Tibetan ༤༠༦ Khmer ៤០៦ Lao ໔໐໖ Burmese ၄၀၆

Digit at this position in famous constants

π — Pi (π): Digit 406 = 7
e — Euler's number (e): Digit 406 = 6
φ — Golden ratio (φ): Digit 406 = 6
√2 — Pythagoras's (√2): Digit 406 = 6
ln 2 — Natural log of 2: Digit 406 = 8
γ — Euler-Mascheroni (γ): Digit 406 = 0

Also seen as

Goldbach decomposition

Goldbach's conjecture says every even integer greater than 2 is the sum of two primes. For 406, here are decompositions:

5 + 401 = 406
17 + 389 = 406
23 + 383 = 406
47 + 359 = 406
53 + 353 = 406
59 + 347 = 406
89 + 317 = 406
113 + 293 = 406

Showing the first eight; more decompositions exist.

Unicode codepoint

Latin Capital Letter Iota

U+0196

Uppercase letter (Lu)

UTF-8 encoding: C6 96 (2 bytes).

Lookup U+0196 on Compart ↗ Lookup on FileFormat.Info ↗

Hex color

#000196

RGB(0, 1, 150)

IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.0.1.150.

Address: 0.0.1.150
Class: reserved
IPv4-mapped IPv6: ::ffff:0.0.1.150

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

Musical pitch

Heard as a frequency, 406 Hz is closest to:

Concert pitch (A4 = 440 Hz): G♯4 (415.3 Hz, -39¢)
Scientific pitch (C4 = 256 Hz): G♯4 (406.4 Hz, -2¢)
Baroque pitch (A4 = 415 Hz): A4 (415 Hz, -38¢)

Food additive (E-number)

On an ingredients label, E406 is Agar, a thickener, stabiliser or emulsifier — a seaweed gelling agent.

E-number reference (Wikipedia) ↗