Number

1,640

1,640 is a composite number, even, a calendar year.

1,640 (one thousand six hundred forty) is an even 4-digit number. It is a composite number with 16 divisors, and factors as 2³ × 5 × 41. Its proper divisors sum to 2,140, more than the number itself, making it an abundant number. Written other ways, in Roman numerals it is MDCXL and in binary, 11001101000.

Abundant Number Gapful Number Odious Number Pernicious Number Practical Number Pronic / Oblong Recamán's Sequence Semiperfect Number Year

Interestingness

★ ★ ★ ☆ ☆

5 notable facts · grade C

1,628 1,629 1,630 1,631 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

less more

Notable events — 1640 AD

Dec 1 Portugal regains independence from Spain under João IV.
Nov 3 England's Long Parliament convenes.
Jun 7 Catalan revolt against Spain breaks out (Reapers' 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: Sunday
January 1, 1640
Ended on: Monday
December 31, 1640
Friday the 13ths: 3
3 Friday the 13ths this year.
Easter Sunday: April 8
Sunday, April 8, 1640
Decade: 1640s
1640–1649
Century: 17th century
1601–1700
Millennium: 2nd millennium
1001–2000
Years ago: 386
386 years before 2026.

In other calendars

Hebrew: 5400 / 5401 AM
Rosh Hashanah falls in September/October.
Islamic Hijri: 1049 / 1050 AH
Lunar calendar; year spans differ from Gregorian.
Chinese: Year of the zodiac:Metal zodiac:Dragon
Sexagenary cycle position 17 of 60. Lunar new year falls in late January / mid-February.
Buddhist Era: 2183 BE
Counted from the parinirvana of the Buddha (Theravada / Thai / Sri Lankan convention).
Persian Solar Hijri: 1018 / 1019 SH
Iranian calendar; Nowruz (new year) falls on the spring equinox.
Ethiopian: 1632 / 1633 ET
Year boundary at Enkutatash (September 11/12).
Indian National (Saka): 1562 / 1561 Saka
Indian national calendar; year starts in March.

Properties

Parity: Even
Digit count: 4
Digit sum: 11
Digit product: 0
Digital root: 2
Palindrome: No
Bit width: 11 bits
Reversed: 461
Recamán's sequence: a(1,300) = 1,640
Square (n²): 2,689,600
Cube (n³): 4,410,944,000
Divisor count: 16
σ(n) — sum of divisors: 3,780
φ(n) — Euler's totient: 640
Sum of prime factors: 52

Primality

Prime factorization: 2 ³ × 5 × 41

Nearest primes: 1,637 (−3) · 1,657 (+17)

Divisors & multiples

All divisors (16)

1 · 2 · 4 · 5 · 8 · 10 · 20 · 40 · 41 · 82 · 164 · 205 · 328 · 410 · 820 (half) · 1640

Aliquot sum (sum of proper divisors): 2,140

Factor pairs (a × b = 1,640)

1 × 1640

2 × 820

4 × 410

5 × 328

8 × 205

10 × 164

20 × 82

40 × 41

First multiples

1,640 · 3,280 (double) · 4,920 · 6,560 · 8,200 · 9,840 · 11,480 · 13,120 · 14,760 · 16,400

Sums & aliquot sequence

As a sum of two squares: 14² + 38² = 22² + 34²

As consecutive integers: 326 + 327 + 328 + 329 + 330 95 + 96 + … + 110 20 + 21 + … + 60

Aliquot sequence: 1,640 → 2,140 → 2,396 → 1,804 → 1,724 → 1,300 → 1,738 → 1,142 → 574 → 434 → 334 → 170 → 154 → 134 → 70 → 74 → 40 — unresolved within range

Continued fraction of √n

√1,640 = [40; (2, 80)]

Period length 2 — the block in parentheses repeats forever.

Representations

In words: one thousand six hundred forty
Ordinal: 1640th
Roman numeral: MDCXL
Binary: 11001101000
Octal: 3150
Hexadecimal: 0x668
Base64: Bmg=
One's complement: 63,895 (16-bit)
Scientific notation: 1.64 × 10³
As a duration: 1,640 s = 27 minutes, 20 seconds

In other bases

ternary (3) 2020202

quaternary (4) 121220

quinary (5) 23030

senary (6) 11332

septenary (7) 4532

nonary (9) 2222

undecimal (11) 1261

duodecimal (12) b48

tridecimal (13) 992

tetradecimal (14) 852

pentadecimal (15) 745

Palindromic in base 3, base 9

As an angle

1,640° = 4 × 360° + 200°

200° ≈ 3.491 rad

Compass bearing: SSW (south-southwest)

Why does a circle have 360 degrees? →

Historical numeral systems

Babylonian (base 60): 𒌋𒌋𒁹𒁹𒁹𒁹𒁹𒁹𒁹 𒌋𒌋
Egyptian hieroglyphic: 𓆼𓍢𓍢𓍢𓍢𓍢𓍢𓎆𓎆𓎆𓎆
Greek (Milesian): ͵αχμʹ
Mayan (base 20): 𝋤·𝋢·𝋠
Chinese: 一千六百四十
Chinese (financial): 壹仟陸佰肆拾

In other modern scripts

Eastern Arabic ١٦٤٠ Devanagari १६४० Bengali ১৬৪০ Tamil ௧௬௪௦ Thai ๑๖๔๐ Tibetan ༡༦༤༠ Khmer ១៦៤០ Lao ໑໖໔໐ Burmese ၁၆၄၀

Digit at this position in famous constants

π — Pi (π): Digit 1,640 = 4
e — Euler's number (e): Digit 1,640 = 5
φ — Golden ratio (φ): Digit 1,640 = 0
√2 — Pythagoras's (√2): Digit 1,640 = 6
ln 2 — Natural log of 2: Digit 1,640 = 1
γ — Euler-Mascheroni (γ): Digit 1,640 = 7

Also seen as

Goldbach decomposition

Goldbach's conjecture says every even integer greater than 2 is the sum of two primes. For 1640, here are decompositions:

3 + 1637 = 1640
13 + 1627 = 1640
19 + 1621 = 1640
31 + 1609 = 1640
43 + 1597 = 1640
61 + 1579 = 1640
73 + 1567 = 1640
97 + 1543 = 1640

Showing the first eight; more decompositions exist.

Unicode codepoint

Arabic-Indic Digit Eight

U+0668

Decimal digit (Nd)

UTF-8 encoding: D9 A8 (2 bytes).

Lookup U+0668 on Compart ↗ Lookup on FileFormat.Info ↗

Hex color

#000668

RGB(0, 6, 104)

IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.0.6.104.

Address: 0.0.6.104
Class: reserved
IPv4-mapped IPv6: ::ffff:0.0.6.104

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

Musical pitch

Heard as a frequency, 1,640 Hz is closest to:

Concert pitch (A4 = 440 Hz): G♯6 (1661.2 Hz, -22¢)
Scientific pitch (C4 = 256 Hz): G♯6 (1625.5 Hz, +15¢)
Baroque pitch (A4 = 415 Hz): A6 (1660 Hz, -21¢)

Position in π

The digit sequence 1640 first appears in π at position 68 of the decimal expansion (the 68ordinal-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 1640 on Pi Search ↗