Number

1,644

1,644 is a composite number, even, a calendar year.

1,644 (one thousand six hundred forty-four) is an even 4-digit number. It is a composite number with 12 divisors, and factors as 2² × 3 × 137. Its proper divisors sum to 2,220, more than the number itself, making it an abundant number. Written other ways, in Roman numerals it is MDCXLIV and in binary, 11001101100.

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

Interestingness

★ ★ ★ ☆ ☆

5 notable facts · grade C

1,632 1,633 1,634 1,635 1,636 1,637 1,638 1,639 1,640 1,641 1,642 1,643 1,644 1,645 1,646 1,647 1,648 1,649 1,650 1,651 1,652 1,653 1,654 1,655 1,656

less more

Notable events — 1644 AD

Apr 25 Beijing falls to rebels; the Ming dynasty ends with the emperor's suicide.
Jul 2 Parliamentarians win at Marston Moor.
Jun 6 The Manchu Qing dynasty enters Beijing.

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

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: Friday
January 1, 1644
Ended on: Saturday
December 31, 1644
Friday the 13ths: 1
One Friday the 13th this year.
Easter Sunday: March 27
Sunday, March 27, 1644
Decade: 1640s
1640–1649
Century: 17th century
1601–1700
Millennium: 2nd millennium
1001–2000
Years ago: 382
382 years before 2026.

In other calendars

Hebrew: 5404 / 5405 AM
Rosh Hashanah falls in September/October.
Islamic Hijri: 1053 / 1054 AH
Lunar calendar; year spans differ from Gregorian.
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: 2187 BE
Counted from the parinirvana of the Buddha (Theravada / Thai / Sri Lankan convention).
Persian Solar Hijri: 1022 / 1023 SH
Iranian calendar; Nowruz (new year) falls on the spring equinox.
Ethiopian: 1636 / 1637 ET
Year boundary at Enkutatash (September 11/12).
Indian National (Saka): 1566 / 1565 Saka
Indian national calendar; year starts in March.

Properties

Parity: Even
Digit count: 4
Digit sum: 15
Digit product: 96
Digital root: 6
Palindrome: No
Bit width: 11 bits
Reversed: 4,461
Recamán's sequence: a(1,028) = 1,644
Square (n²): 2,702,736
Cube (n³): 4,443,297,984
Divisor count: 12
σ(n) — sum of divisors: 3,864
φ(n) — Euler's totient: 544
Sum of prime factors: 144

Primality

Prime factorization: 2 ² × 3 × 137

Nearest primes: 1,637 (−7) · 1,657 (+13)

Divisors & multiples

All divisors (12)

1 · 2 · 3 · 4 · 6 · 12 · 137 · 274 · 411 · 548 · 822 (half) · 1644

Aliquot sum (sum of proper divisors): 2,220

Factor pairs (a × b = 1,644)

1 × 1644

2 × 822

3 × 548

4 × 411

6 × 274

12 × 137

First multiples

1,644 · 3,288 (double) · 4,932 · 6,576 · 8,220 · 9,864 · 11,508 · 13,152 · 14,796 · 16,440

Sums & aliquot sequence

As consecutive integers: 547 + 548 + 549 202 + 203 + … + 209 57 + 58 + … + 80

Aliquot sequence: 1,644 → 2,220 → 4,164 → 5,580 → 11,892 → 15,884 → 16,120 → 24,200 → 37,645 → 7,535 → 2,401 → 400 → 561 → 303 → 105 → 87 → 33 — unresolved within range

Continued fraction of √n

√1,644 = [40; (1, 1, 4, 1, 9, 3, 7, 20, 7, 3, 9, 1, 4, 1, 1, 80)]

Period length 16 — the block in parentheses repeats forever.

Representations

In words: one thousand six hundred forty-four
Ordinal: 1644th
Roman numeral: MDCXLIV
Binary: 11001101100
Octal: 3154
Hexadecimal: 0x66C
Base64: Bmw=
One's complement: 63,891 (16-bit)
Scientific notation: 1.644 × 10³
As a duration: 1,644 s = 27 minutes, 24 seconds

In other bases

ternary (3) 2020220

quaternary (4) 121230

quinary (5) 23034

senary (6) 11340

septenary (7) 4536

nonary (9) 2226

undecimal (11) 1265

duodecimal (12) b50

tridecimal (13) 996

tetradecimal (14) 856

pentadecimal (15) 749

As an angle

1,644° = 4 × 360° + 204°

204° ≈ 3.56 rad

Compass bearing: SSW (south-southwest)

Why does a circle have 360 degrees? →

Historical numeral systems

Babylonian (base 60): 𒌋𒌋𒁹𒁹𒁹𒁹𒁹𒁹𒁹 𒌋𒌋𒁹𒁹𒁹𒁹
Egyptian hieroglyphic: 𓆼𓍢𓍢𓍢𓍢𓍢𓍢𓎆𓎆𓎆𓎆𓏺𓏺𓏺𓏺
Greek (Milesian): ͵αχμδʹ
Mayan (base 20): 𝋤·𝋢·𝋤
Chinese: 一千六百四十四
Chinese (financial): 壹仟陸佰肆拾肆

In other modern scripts

Eastern Arabic ١٦٤٤ Devanagari १६४४ Bengali ১৬৪৪ Tamil ௧௬௪௪ Thai ๑๖๔๔ Tibetan ༡༦༤༤ Khmer ១៦៤៤ Lao ໑໖໔໔ Burmese ၁၆၄၄

Digit at this position in famous constants

π — Pi (π): Digit 1,644 = 7
e — Euler's number (e): Digit 1,644 = 3
φ — Golden ratio (φ): Digit 1,644 = 1
√2 — Pythagoras's (√2): Digit 1,644 = 5
ln 2 — Natural log of 2: Digit 1,644 = 8
γ — Euler-Mascheroni (γ): Digit 1,644 = 0

Also seen as

Goldbach decomposition

Goldbach's conjecture says every even integer greater than 2 is the sum of two primes. For 1644, here are decompositions:

7 + 1637 = 1644
17 + 1627 = 1644
23 + 1621 = 1644
31 + 1613 = 1644
37 + 1607 = 1644
43 + 1601 = 1644
47 + 1597 = 1644
61 + 1583 = 1644

Showing the first eight; more decompositions exist.

Unicode codepoint

Arabic Thousands Separator

U+066C

Other punctuation (Po)

UTF-8 encoding: D9 AC (2 bytes).

Lookup U+066C on Compart ↗ Lookup on FileFormat.Info ↗

Hex color

#00066C

RGB(0, 6, 108)

IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.0.6.108.

Address: 0.0.6.108
Class: reserved
IPv4-mapped IPv6: ::ffff:0.0.6.108

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

Musical pitch

Heard as a frequency, 1,644 Hz is closest to:

Concert pitch (A4 = 440 Hz): G♯6 (1661.2 Hz, -18¢)
Scientific pitch (C4 = 256 Hz): G♯6 (1625.5 Hz, +20¢)
Baroque pitch (A4 = 415 Hz): A6 (1660 Hz, -17¢)

Position in π

The digit sequence 1644 first appears in π at position 3,370 of the decimal expansion (the 3,370ordinal-suffix:th digit after the integer 3).

Search range: the first 1,000,000 fractional digits of π. Any 6-digit-or-shorter string is virtually guaranteed to appear in there — the more interesting signal is the position.

Look up 1644 on Pi Search ↗