Number

564

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

564 (five hundred sixty-four) is an even 3-digit number. It is a composite number with 12 divisors, and factors as 2² × 3 × 47. Its proper divisors sum to 780, more than the number itself, making it an abundant number. Written other ways, in Roman numerals it is DLXIV and in binary, 1000110100.

Abundant Number Arithmetic Number Cube-Free Evil Number Recamán's Sequence Refactorable Number Semiperfect Number Year

Interestingness

★ ★ ★ ☆ ☆

5 notable facts · grade C

552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576

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Historical context — 564 AD

Calendar year

Year 564 (DLXIV) was a leap year starting on Tuesday of the Julian calendar.

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

Historical context — 564 BC

Calendar year

The year 564 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: Leap year
Divisible by 4 and not by 100; February has 29 days.
Days in year: 366
ISO weeks: 52
Started on: Sunday
January 1, 564
Ended on: Monday
December 31, 564
Friday the 13ths: 3
3 Friday the 13ths this year.
Decade: 560s
560–569
Century: 6th century
501–600
Millennium: 1st millennium
1–1000
Years ago: 1,462
1462 years before 2026.

In other calendars

Hebrew: 4324 / 4325 AM
Rosh Hashanah falls in September/October.
Chinese: Year of the zodiac:Wood zodiac:Monkey
Sexagenary cycle position 21 of 60. Lunar new year falls in late January / mid-February.
Buddhist Era: 1107 BE
Counted from the parinirvana of the Buddha (Theravada / Thai / Sri Lankan convention).
Ethiopian: 556 / 557 ET
Year boundary at Enkutatash (September 11/12).
Indian National (Saka): 486 / 485 Saka
Indian national calendar; year starts in March.

Properties

Parity: Even
Digit count: 3
Digit sum: 15
Digit product: 120
Digital root: 6
Palindrome: No
Bit width: 10 bits
Reversed: 465
Recamán's sequence: a(1,131) = 564
Square (n²): 318,096
Cube (n³): 179,406,144
Divisor count: 12
σ(n) — sum of divisors: 1,344
φ(n) — Euler's totient: 184
Sum of prime factors: 54

Primality

Prime factorization: 2 ² × 3 × 47

Nearest primes: 563 (−1) · 569 (+5)

Divisors & multiples

All divisors (12)

1 · 2 · 3 · 4 · 6 · 12 · 47 · 94 · 141 · 188 · 282 (half) · 564

Aliquot sum (sum of proper divisors): 780

Factor pairs (a × b = 564)

1 × 564

2 × 282

3 × 188

4 × 141

6 × 94

12 × 47

First multiples

564 · 1,128 (double) · 1,692 · 2,256 · 2,820 · 3,384 · 3,948 · 4,512 · 5,076 · 5,640

Sums & aliquot sequence

As consecutive integers: 187 + 188 + 189 67 + 68 + … + 74 12 + 13 + … + 35

Aliquot sequence: 564 → 780 → 1,572 → 2,124 → 3,336 → 5,064 → 7,656 → 13,944 → 26,376 → 49,464 → 88,536 → 187,944 → 295,896 → 443,904 → 812,340 → 1,652,304 → 2,767,056 — unresolved within range

Continued fraction of √n

√564 = [23; (1, 2, 1, 46)]

Period length 4 — the block in parentheses repeats forever.

Representations

In words: five hundred sixty-four
Ordinal: 564th
Roman numeral: DLXIV
Binary: 1000110100
Octal: 1064
Hexadecimal: 0x234
Base64: AjQ=
One's complement: 64,971 (16-bit)
Scientific notation: 5.64 × 10²
As a duration: 564 s = 9 minutes, 24 seconds

In other bases

ternary (3) 202220

quaternary (4) 20310

quinary (5) 4224

senary (6) 2340

septenary (7) 1434

nonary (9) 686

undecimal (11) 473

duodecimal (12) 3b0

tridecimal (13) 345

tetradecimal (14) 2c4

pentadecimal (15) 279

Palindromic in base 5, base 9

As an angle

564° = 1 × 360° + 204°

204° ≈ 3.56 rad

Compass bearing: SSW (south-southwest)

Why does a circle have 360 degrees? →

Historical numeral systems

Babylonian (base 60): 𒁹𒁹𒁹𒁹𒁹𒁹𒁹𒁹𒁹 𒌋𒌋𒁹𒁹𒁹𒁹
Egyptian hieroglyphic: 𓍢𓍢𓍢𓍢𓍢𓎆𓎆𓎆𓎆𓎆𓎆𓏺𓏺𓏺𓏺
Greek (Milesian): φξδʹ
Mayan (base 20): 𝋡·𝋨·𝋤
Chinese: 五百六十四
Chinese (financial): 伍佰陸拾肆

In other modern scripts

Eastern Arabic ٥٦٤ Devanagari ५६४ Bengali ৫৬৪ Tamil ௫௬௪ Thai ๕๖๔ Tibetan ༥༦༤ Khmer ៥៦៤ Lao ໕໖໔ Burmese ၅၆၄

Digit at this position in famous constants

π — Pi (π): Digit 564 = 3
e — Euler's number (e): Digit 564 = 6
φ — Golden ratio (φ): Digit 564 = 1
√2 — Pythagoras's (√2): Digit 564 = 1
ln 2 — Natural log of 2: Digit 564 = 9
γ — Euler-Mascheroni (γ): Digit 564 = 4

Also seen as

Goldbach decomposition

Goldbach's conjecture says every even integer greater than 2 is the sum of two primes. For 564, here are decompositions:

7 + 557 = 564
17 + 547 = 564
23 + 541 = 564
41 + 523 = 564
43 + 521 = 564
61 + 503 = 564
73 + 491 = 564
97 + 467 = 564

Showing the first eight; more decompositions exist.

Unicode codepoint

Latin Small Letter L With Curl

U+0234

Lowercase letter (Ll)

UTF-8 encoding: C8 B4 (2 bytes).

Lookup U+0234 on Compart ↗ Lookup on FileFormat.Info ↗

Hex color

#000234

RGB(0, 2, 52)

IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.0.2.52.

Address: 0.0.2.52
Class: reserved
IPv4-mapped IPv6: ::ffff:0.0.2.52

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

NANP area code 564

The number 564 is an active NANP area code (North American Numbering Plan).

Primary area: Western Washington
Region: Washington
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 564 ↗

Musical pitch

Heard as a frequency, 564 Hz is closest to:

Concert pitch (A4 = 440 Hz): C♯5 (554.4 Hz, +30¢)
Scientific pitch (C4 = 256 Hz): D5 (574.7 Hz, -33¢)
Baroque pitch (A4 = 415 Hz): D5 (554 Hz, +31¢)