Number

1,664

1,664 is a composite number, even, a calendar year.

1,664 (one thousand six hundred sixty-four) is an even 4-digit number. It is a composite number with 16 divisors, and factors as 2⁷ × 13. Its proper divisors sum to 1,906, more than the number itself, making it an abundant number. Written other ways, in Roman numerals it is MDCLXIV and in binary, 11010000000.

Abundant Number Odious Number Pernicious Number Practical Number Recamán's Sequence Refactorable Number Semiperfect Number Year

Interestingness

★ ★ ☆ ☆ ☆

4 notable facts · grade D

1,652 1,653 1,654 1,655 1,656 1,657 1,658 1,659 1,660 1,661 1,662 1,663 1,664 1,665 1,666 1,667 1,668 1,669 1,670 1,671 1,672 1,673 1,674 1,675 1,676

less more

Notable events — 1664 AD

Aug 27 The Dutch surrender New Amsterdam to the English; it is renamed New York.
Aug 1 Ottoman forces are checked at St. Gotthard, ending their westward advance.
Dec 17 An English fleet seizes Dutch posts on the African coast, escalating to war.

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: Tuesday
January 1, 1664
Ended on: Wednesday
December 31, 1664
Friday the 13ths: 1
One Friday the 13th this year.
Easter Sunday: April 13
Sunday, April 13, 1664
Decade: 1660s
1660–1669
Century: 17th century
1601–1700
Millennium: 2nd millennium
1001–2000
Years ago: 362
362 years before 2026.

In other calendars

Hebrew: 5424 / 5425 AM
Rosh Hashanah falls in September/October.
Islamic Hijri: 1074 / 1075 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: 2207 BE
Counted from the parinirvana of the Buddha (Theravada / Thai / Sri Lankan convention).
Persian Solar Hijri: 1042 / 1043 SH
Iranian calendar; Nowruz (new year) falls on the spring equinox.
Ethiopian: 1656 / 1657 ET
Year boundary at Enkutatash (September 11/12).
Indian National (Saka): 1586 / 1585 Saka
Indian national calendar; year starts in March.

Properties

Parity: Even
Digit count: 4
Digit sum: 17
Digit product: 144
Digital root: 8
Palindrome: No
Bit width: 11 bits
Reversed: 4,661
Recamán's sequence: a(796) = 1,664
Square (n²): 2,768,896
Cube (n³): 4,607,442,944
Divisor count: 16
σ(n) — sum of divisors: 3,570
φ(n) — Euler's totient: 768
Sum of prime factors: 27

Primality

Prime factorization: 2 ⁷ × 13

Nearest primes: 1,663 (−1) · 1,667 (+3)

Divisors & multiples

All divisors (16)

1 · 2 · 4 · 8 · 13 · 16 · 26 · 32 · 52 · 64 · 104 · 128 · 208 · 416 · 832 (half) · 1664

Aliquot sum (sum of proper divisors): 1,906

Factor pairs (a × b = 1,664)

1 × 1664

2 × 832

4 × 416

8 × 208

13 × 128

16 × 104

26 × 64

32 × 52

First multiples

1,664 · 3,328 (double) · 4,992 · 6,656 · 8,320 · 9,984 · 11,648 · 13,312 · 14,976 · 16,640

Sums & aliquot sequence

As a sum of two squares: 8² + 40²

As consecutive integers: 122 + 123 + … + 134

Aliquot sequence: 1,664 → 1,906 → 956 → 724 → 550 → 566 → 286 → 218 → 112 → 136 → 134 → 70 → 74 → 40 → 50 → 43 → 1 — unresolved within range

Continued fraction of √n

√1,664 = [40; (1, 3, 1, 4, 3, 2, 1, 19, 1, 2, 3, 4, 1, 3, 1, 80)]

Period length 16 — the block in parentheses repeats forever.

Representations

In words: one thousand six hundred sixty-four
Ordinal: 1664th
Roman numeral: MDCLXIV
Binary: 11010000000
Octal: 3200
Hexadecimal: 0x680
Base64: BoA=
One's complement: 63,871 (16-bit)
Scientific notation: 1.664 × 10³
As a duration: 1,664 s = 27 minutes, 44 seconds

In other bases

ternary (3) 2021122

quaternary (4) 122000

quinary (5) 23124

senary (6) 11412

septenary (7) 4565

nonary (9) 2248

undecimal (11) 1283

duodecimal (12) b68

tridecimal (13) 9b0

tetradecimal (14) 86c

pentadecimal (15) 75e

As an angle

1,664° = 4 × 360° + 224°

224° ≈ 3.91 rad

Compass bearing: SW (southwest)

Why does a circle have 360 degrees? →

Historical numeral systems

Babylonian (base 60): 𒌋𒌋𒁹𒁹𒁹𒁹𒁹𒁹𒁹 𒌋𒌋𒌋𒌋𒁹𒁹𒁹𒁹
Egyptian hieroglyphic: 𓆼𓍢𓍢𓍢𓍢𓍢𓍢𓎆𓎆𓎆𓎆𓎆𓎆𓏺𓏺𓏺𓏺
Greek (Milesian): ͵αχξδʹ
Mayan (base 20): 𝋤·𝋣·𝋤
Chinese: 一千六百六十四
Chinese (financial): 壹仟陸佰陸拾肆

In other modern scripts

Eastern Arabic ١٦٦٤ Devanagari १६६४ Bengali ১৬৬৪ Tamil ௧௬௬௪ Thai ๑๖๖๔ Tibetan ༡༦༦༤ Khmer ១៦៦៤ Lao ໑໖໖໔ Burmese ၁၆၆၄

Digit at this position in famous constants

π — Pi (π): Digit 1,664 = 5
e — Euler's number (e): Digit 1,664 = 6
φ — Golden ratio (φ): Digit 1,664 = 6
√2 — Pythagoras's (√2): Digit 1,664 = 4
ln 2 — Natural log of 2: Digit 1,664 = 0
γ — Euler-Mascheroni (γ): Digit 1,664 = 8

Also seen as

Goldbach decomposition

Goldbach's conjecture says every even integer greater than 2 is the sum of two primes. For 1664, here are decompositions:

7 + 1657 = 1664
37 + 1627 = 1664
43 + 1621 = 1664
67 + 1597 = 1664
97 + 1567 = 1664
181 + 1483 = 1664
193 + 1471 = 1664
211 + 1453 = 1664

Showing the first eight; more decompositions exist.

Unicode codepoint

Arabic Letter Beheh

U+0680

Other letter (Lo)

UTF-8 encoding: DA 80 (2 bytes).

Lookup U+0680 on Compart ↗ Lookup on FileFormat.Info ↗

Hex color

#000680

RGB(0, 6, 128)

IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.0.6.128.

Address: 0.0.6.128
Class: reserved
IPv4-mapped IPv6: ::ffff:0.0.6.128

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

Musical pitch

Heard as a frequency, 1,664 Hz is closest to:

Concert pitch (A4 = 440 Hz): G♯6 (1661.2 Hz, +3¢)
Scientific pitch (C4 = 256 Hz): G♯6 (1625.5 Hz, +41¢)
Baroque pitch (A4 = 415 Hz): A6 (1660 Hz, +4¢)

Position in π

The digit sequence 1664 first appears in π at position 4,742 of the decimal expansion (the 4,742ordinal-suffix:nd 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 1664 on Pi Search ↗