Number

644

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

644 (six hundred forty-four) is an even 3-digit number. It is a composite number with 12 divisors, and factors as 2² × 7 × 23. Its proper divisors sum to 700, more than the number itself, making it an abundant number. Written other ways, in Roman numerals it is DCXLIV and in binary, 1010000100.

Abundant Number Arithmetic Number Cube-Free Happy Number Harshad / Niven Odious Number Pernicious Number Perrin Number Practical Number Recamán's Sequence Semiperfect Number Year

Interestingness

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8 notable facts · grade A

632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656

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Historical context — 644 AD

Calendar year

Year 644 (DCXLIV) was a leap year starting on Thursday of the Julian calendar.

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

Historical context — 644 BC

Calendar year

The year 644 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: Monday
January 1, 644
Ended on: Tuesday
December 31, 644
Friday the 13ths: 2
2 Friday the 13ths this year.
Decade: 640s
640–649
Century: 7th century
601–700
Millennium: 1st millennium
1–1000
Years ago: 1,382
1382 years before 2026.

In other calendars

Hebrew: 4404 / 4405 AM
Rosh Hashanah falls in September/October.
Islamic Hijri: 23 / 24 AH
Lunar calendar; year spans differ from Gregorian.
Chinese: Year of the zodiac:Wood zodiac:Dragon
Sexagenary cycle position 41 of 60. Lunar new year falls in late January / mid-February.
Buddhist Era: 1187 BE
Counted from the parinirvana of the Buddha (Theravada / Thai / Sri Lankan convention).
Persian Solar Hijri: 22 / 23 SH
Iranian calendar; Nowruz (new year) falls on the spring equinox.
Ethiopian: 636 / 637 ET
Year boundary at Enkutatash (September 11/12).
Indian National (Saka): 566 / 565 Saka
Indian national calendar; year starts in March.

Properties

Parity: Even
Digit count: 3
Digit sum: 14
Digit product: 96
Digital root: 5
Palindrome: No
Bit width: 10 bits
Reversed: 446
Recamán's sequence: a(2,336) = 644
Square (n²): 414,736
Cube (n³): 267,089,984
Divisor count: 12
σ(n) — sum of divisors: 1,344
φ(n) — Euler's totient: 264
Sum of prime factors: 34

Primality

Prime factorization: 2 ² × 7 × 23

Nearest primes: 643 (−1) · 647 (+3)

Divisors & multiples

All divisors (12)

1 · 2 · 4 · 7 · 14 · 23 · 28 · 46 · 92 · 161 · 322 (half) · 644

Aliquot sum (sum of proper divisors): 700

Factor pairs (a × b = 644)

1 × 644

2 × 322

4 × 161

7 × 92

14 × 46

23 × 28

First multiples

644 · 1,288 (double) · 1,932 · 2,576 · 3,220 · 3,864 · 4,508 · 5,152 · 5,796 · 6,440

Sums & aliquot sequence

As consecutive integers: 89 + 90 + … + 95 77 + 78 + … + 84 17 + 18 + … + 39

Aliquot sequence: 644 → 700 → 1,036 → 1,092 → 2,044 → 2,100 → 4,844 → 4,900 → 7,469 → 1,939 → 285 → 195 → 141 → 51 → 21 → 11 → 1 — unresolved within range

Continued fraction of √n

√644 = [25; (2, 1, 1, 1, 6, 1, 1, 1, 2, 50)]

Period length 10 — the block in parentheses repeats forever.

Representations

In words: six hundred forty-four
Ordinal: 644th
Roman numeral: DCXLIV
Binary: 1010000100
Octal: 1204
Hexadecimal: 0x284
Base64: AoQ=
One's complement: 64,891 (16-bit)
Scientific notation: 6.44 × 10²
As a duration: 644 s = 10 minutes, 44 seconds

In other bases

ternary (3) 212212

quaternary (4) 22010

quinary (5) 10034

senary (6) 2552

septenary (7) 1610

nonary (9) 785

undecimal (11) 536

duodecimal (12) 458

tridecimal (13) 3a7

tetradecimal (14) 340

pentadecimal (15) 2ce

Palindromic in base 3, base 6

As an angle

644° = 1 × 360° + 284°

284° ≈ 4.957 rad

Compass bearing: WNW (west-northwest)

Why does a circle have 360 degrees? →

Historical numeral systems

Babylonian (base 60): 𒌋 𒌋𒌋𒌋𒌋𒁹𒁹𒁹𒁹
Egyptian hieroglyphic: 𓍢𓍢𓍢𓍢𓍢𓍢𓎆𓎆𓎆𓎆𓏺𓏺𓏺𓏺
Greek (Milesian): χμδʹ
Mayan (base 20): 𝋡·𝋬·𝋤
Chinese: 六百四十四
Chinese (financial): 陸佰肆拾肆

In other modern scripts

Eastern Arabic ٦٤٤ Devanagari ६४४ Bengali ৬৪৪ Tamil ௬௪௪ Thai ๖๔๔ Tibetan ༦༤༤ Khmer ៦៤៤ Lao ໖໔໔ Burmese ၆၄၄

Digit at this position in famous constants

π — Pi (π): Digit 644 = 6
e — Euler's number (e): Digit 644 = 4
φ — Golden ratio (φ): Digit 644 = 7
√2 — Pythagoras's (√2): Digit 644 = 4
ln 2 — Natural log of 2: Digit 644 = 4
γ — Euler-Mascheroni (γ): Digit 644 = 9

Also seen as

Goldbach decomposition

Goldbach's conjecture says every even integer greater than 2 is the sum of two primes. For 644, here are decompositions:

3 + 641 = 644
13 + 631 = 644
31 + 613 = 644
37 + 607 = 644
43 + 601 = 644
67 + 577 = 644
73 + 571 = 644
97 + 547 = 644

Showing the first eight; more decompositions exist.

Unicode codepoint

Latin Small Letter Dotless J With Stroke And Hook

U+0284

Lowercase letter (Ll)

UTF-8 encoding: CA 84 (2 bytes).

Lookup U+0284 on Compart ↗ Lookup on FileFormat.Info ↗

Hex color

#000284

RGB(0, 2, 132)

IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.0.2.132.

Address: 0.0.2.132
Class: reserved
IPv4-mapped IPv6: ::ffff:0.0.2.132

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

Musical pitch

Heard as a frequency, 644 Hz is closest to:

Concert pitch (A4 = 440 Hz): E5 (659.3 Hz, -41¢)
Scientific pitch (C4 = 256 Hz): E5 (645.1 Hz, -3¢)
Baroque pitch (A4 = 415 Hz): F5 (658.8 Hz, -39¢)