Number

400

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

Abundant Number Gapful Number Harshad / Niven Odious Number Perfect Square Pernicious Number Powerful Number Practical Number Recamán's Sequence Self Number Semiperfect Number Year

Historical context — 400 AD

Calendar year

Year 400 (CD) was a leap year starting on Sunday of the Julian calendar.

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

Historical context — 400 BC

Calendar year

Year 400 BC was a year of the pre-Julian Roman calendar.

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 400 (Gregorian leap-year rule exception to the century rule).
Days in year: 366
ISO weeks: 52
Started on: Saturday
January 1, 400
Ended on: Sunday
December 31, 400
Friday the 13ths: 1
One Friday the 13th this year.
Decade: 400s
400–409
Century: 4th century
301–400
Millennium: 1st millennium
1–1000
Years ago: 1,626
1626 years before 2026.

In other calendars

Hebrew: 4160 / 4161 AM
Rosh Hashanah falls in September/October.
Chinese: Year of the zodiac:Metal zodiac:Rat
Sexagenary cycle position 37 of 60. Lunar new year falls in late January / mid-February.
Buddhist Era: 943 BE
Counted from the parinirvana of the Buddha (Theravada / Thai / Sri Lankan convention).
Ethiopian: 392 / 393 ET
Year boundary at Enkutatash (September 11/12).
Indian National (Saka): 322 / 321 Saka
Indian national calendar; year starts in March.

Properties

Parity: Even
Digit count: 3
Digit sum: 4
Digit product: 0
Digital root: 4
Palindrome: No
Bit width: 9 bits
Reversed: 4
Recamán's sequence: a(2,452) = 400
Square (n²): 160,000
Cube (n³): 64,000,000
Square root (√n): 20
Divisor count: 15
σ(n) — sum of divisors: 961
φ(n) — Euler's totient: 160
Sum of prime factors: 18

Primality

Prime factorization: 2 ⁴ × 5 ²

Nearest primes: 397 (−3) · 401 (+1)

Divisors & multiples

All divisors (15)

1 · 2 · 4 · 5 · 8 · 10 · 16 · 20 · 25 · 40 · 50 · 80 · 100 · 200 (half) · 400

Aliquot sum (sum of proper divisors): 561

Factor pairs (a × b = 400)

1 × 400

2 × 200

4 × 100

5 × 80

8 × 50

10 × 40

16 × 25

20 × 20

First multiples

400 · 800 (double) · 1,200 · 1,600 · 2,000 · 2,400 · 2,800 · 3,200 · 3,600 · 4,000

Sums & aliquot sequence

As a sum of two squares: 0² + 20² = 12² + 16²

As consecutive integers: 78 + 79 + 80 + 81 + 82 4 + 5 + … + 28

Aliquot sequence: 400 → 561 → 303 → 105 → 87 → 33 → 15 → 9 → 4 → 3 → 1 → 0 — terminates at zero

Representations

In words: four hundred
Ordinal: 400th
Roman numeral: CD
Binary: 110010000
Octal: 620
Hexadecimal: 0x190
Base64: AZA=
One's complement: 65,135 (16-bit)

In other bases

ternary (3) 112211

quaternary (4) 12100

quinary (5) 3100

senary (6) 1504

septenary (7) 1111

nonary (9) 484

undecimal (11) 334

duodecimal (12) 294

tridecimal (13) 24a

tetradecimal (14) 208

pentadecimal (15) 1ba

Historical numeral systems

Babylonian (base 60): 𒁹𒁹𒁹𒁹𒁹𒁹 𒌋𒌋𒌋𒌋
Egyptian hieroglyphic: 𓍢𓍢𓍢𓍢
Greek (Milesian): υʹ
Mayan (base 20): 𝋡·𝋠·𝋠
Chinese: 四百
Chinese (financial): 肆佰

In other modern scripts

Eastern Arabic ٤٠٠ Devanagari ४०० Bengali ৪০০ Tamil ௪௦௦ Thai ๔๐๐ Tibetan ༤༠༠ Khmer ៤០០ Lao ໔໐໐ Burmese ၄၀၀

Digit at this position in famous constants

π — Pi (π): Digit 400 = 9
e — Euler's number (e): Digit 400 = 1
φ — Golden ratio (φ): Digit 400 = 8
√2 — Pythagoras's (√2): Digit 400 = 7
ln 2 — Natural log of 2: Digit 400 = 5
γ — Euler-Mascheroni (γ): Digit 400 = 1

Also seen as

Goldbach decomposition

Goldbach's conjecture says every even integer greater than 2 is the sum of two primes. For 400, here are decompositions:

3 + 397 = 400
11 + 389 = 400
17 + 383 = 400
41 + 359 = 400
47 + 353 = 400
53 + 347 = 400
83 + 317 = 400
89 + 311 = 400

Showing the first eight; more decompositions exist.

Unicode codepoint

Latin Capital Letter Open E

U+0190

Uppercase letter (Lu)

UTF-8 encoding: C6 90 (2 bytes).

Lookup U+0190 on Compart ↗ Lookup on FileFormat.Info ↗

HTTP status code

HTTP 400 Bad Request — Server cannot or will not process the request due to a client error.

4xx class: Client Error.

Hex color

#000190

RGB(0, 1, 144)

IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.0.1.144.

Address: 0.0.1.144
Class: reserved
IPv4-mapped IPv6: ::ffff:0.0.1.144

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