Number

2,040

2,040 is a composite number, even, a calendar year.

2,040 (two thousand forty) is an even 4-digit number. It is a composite number with 32 divisors, and factors as 2³ × 3 × 5 × 17. Its proper divisors sum to 4,440, more than the number itself, making it an abundant number. Written other ways, in Roman numerals it is MMXL and in binary, 11111111000.

Abundant Number Evil Number Gapful Number Harshad / Niven Practical Number Recamán's Sequence Semiperfect Number Year

Interestingness

★ ★ ★ ☆ ☆

5 notable facts · grade C

2,028 2,029 2,030 2,031 2,032 2,033 2,034 2,035 2,036 2,037 2,038 2,039 2,040 2,041 2,042 2,043 2,044 2,045 2,046 2,047 2,048 2,049 2,050 2,051 2,052

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Historical context — 2040 AD

Current millennium spanning the years 2001 to 3000

The third millennium of the Anno Domini or Common Era is the current millennium spanning the years 2001 to 3000.

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, 2040
Ended on: Monday
December 31, 2040
Friday the 13ths: 3
3 Friday the 13ths this year.
Easter Sunday: April 1
Sunday, April 1, 2040
Decade: 2040s
2040–2049
Century: 21st century
2001–2100
Millennium: 3rd millennium
2001–3000
Years until: 14
14 years after 2026.
US presidential election: Yes
US holds a presidential election in years divisible by 4 starting from 1788.
Summer Olympics: Yes

In other calendars

Hebrew: 5800 / 5801 AM
Rosh Hashanah falls in September/October.
Islamic Hijri: 1461 / 1462 AH
Lunar calendar; year spans differ from Gregorian.
Chinese: Year of the zodiac:Metal zodiac:Monkey
Sexagenary cycle position 57 of 60. Lunar new year falls in late January / mid-February.
Buddhist Era: 2583 BE
Counted from the parinirvana of the Buddha (Theravada / Thai / Sri Lankan convention).
Persian Solar Hijri: 1418 / 1419 SH
Iranian calendar; Nowruz (new year) falls on the spring equinox.
Ethiopian: 2032 / 2033 ET
Year boundary at Enkutatash (September 11/12).
Indian National (Saka): 1962 / 1961 Saka
Indian national calendar; year starts in March.
Japanese: Reiwa 22
Reign-era counting from the start of each emperor's reign.

Properties

Parity: Even
Digit count: 4
Digit sum: 6
Digit product: 0
Digital root: 6
Palindrome: No
Bit width: 11 bits
Reversed: 402
Recamán's sequence: a(3,671) = 2,040
Square (n²): 4,161,600
Cube (n³): 8,489,664,000
Divisor count: 32
σ(n) — sum of divisors: 6,480
φ(n) — Euler's totient: 512
Sum of prime factors: 31

Primality

Prime factorization: 2 ³ × 3 × 5 × 17

Nearest primes: 2,039 (−1) · 2,053 (+13)

Divisors & multiples

All divisors (32)

1 · 2 · 3 · 4 · 5 · 6 · 8 · 10 · 12 · 15 · 17 · 20 · 24 · 30 · 34 · 40 · 51 · 60 · 68 · 85 · 102 · 120 · 136 · 170 · 204 · 255 · 340 · 408 · 510 · 680 · 1020 (half) · 2040

Aliquot sum (sum of proper divisors): 4,440

Factor pairs (a × b = 2,040)

1 × 2040

2 × 1020

3 × 680

4 × 510

5 × 408

6 × 340

8 × 255

10 × 204

12 × 170

15 × 136

17 × 120

20 × 102

24 × 85

30 × 68

34 × 60

40 × 51

First multiples

2,040 · 4,080 (double) · 6,120 · 8,160 · 10,200 · 12,240 · 14,280 · 16,320 · 18,360 · 20,400

Sums & aliquot sequence

As consecutive integers: 679 + 680 + 681 406 + 407 + 408 + 409 + 410 129 + 130 + … + 143 120 + 121 + … + 135

Aliquot sequence: 2,040 → 4,440 → 9,240 → 25,320 → 51,000 → 117,480 → 271,320 → 765,480 → 1,531,320 → 3,721,800 → 7,817,640 → 15,635,640 → 32,899,560 → 65,799,480 → 139,098,120 → 349,027,320 → 699,333,000 — unresolved within range

Continued fraction of √n

√2,040 = [45; (6, 90)]

Period length 2 — the block in parentheses repeats forever.

Representations

In words: two thousand forty
Ordinal: 2040th
Roman numeral: MMXL
Binary: 11111111000
Octal: 3770
Hexadecimal: 0x7F8
Base64: B/g=
One's complement: 63,495 (16-bit)
Scientific notation: 2.04 × 10³
As a duration: 2,040 s = 34 minutes

In other bases

ternary (3) 2210120

quaternary (4) 133320

quinary (5) 31130

senary (6) 13240

septenary (7) 5643

nonary (9) 2716

undecimal (11) 1595

duodecimal (12) 1220

tridecimal (13) c0c

tetradecimal (14) a5a

pentadecimal (15) 910

Palindromic in base 13, base 14

As an angle

2,040° = 5 × 360° + 240°

240° ≈ 4.189 rad

Compass bearing: WSW (west-southwest)

Why does a circle have 360 degrees? →

Historical numeral systems

Babylonian (base 60): 𒌋𒌋𒌋𒁹𒁹𒁹𒁹 ·
Egyptian hieroglyphic: 𓆼𓆼𓎆𓎆𓎆𓎆
Greek (Milesian): ͵βμʹ
Mayan (base 20): 𝋥·𝋢·𝋠
Chinese: 二千零四十
Chinese (financial): 貳仟零肆拾

In other modern scripts

Eastern Arabic ٢٠٤٠ Devanagari २०४० Bengali ২০৪০ Tamil ௨௦௪௦ Thai ๒๐๔๐ Tibetan ༢༠༤༠ Khmer ២០៤០ Lao ໒໐໔໐ Burmese ၂၀၄၀

Digit at this position in famous constants

π — Pi (π): Digit 2,040 = 2
e — Euler's number (e): Digit 2,040 = 9
φ — Golden ratio (φ): Digit 2,040 = 5
√2 — Pythagoras's (√2): Digit 2,040 = 3
ln 2 — Natural log of 2: Digit 2,040 = 9
γ — Euler-Mascheroni (γ): Digit 2,040 = 0

Also seen as

Goldbach decomposition

Goldbach's conjecture says every even integer greater than 2 is the sum of two primes. For 2040, here are decompositions:

11 + 2029 = 2040
13 + 2027 = 2040
23 + 2017 = 2040
29 + 2011 = 2040
37 + 2003 = 2040
41 + 1999 = 2040
43 + 1997 = 2040
47 + 1993 = 2040

Showing the first eight; more decompositions exist.

Unicode codepoint

Nko Comma

U+07F8

Other punctuation (Po)

UTF-8 encoding: DF B8 (2 bytes).

Lookup U+07F8 on Compart ↗ Lookup on FileFormat.Info ↗

Hex color

#0007F8

RGB(0, 7, 248)

IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.0.7.248.

Address: 0.0.7.248
Class: reserved
IPv4-mapped IPv6: ::ffff:0.0.7.248

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

Musical pitch

Heard as a frequency, 2,040 Hz is closest to:

Concert pitch (A4 = 440 Hz): C7 (2093 Hz, -44¢)
Scientific pitch (C4 = 256 Hz): C7 (2048 Hz, -7¢)
Baroque pitch (A4 = 415 Hz): C♯7 (2091.5 Hz, -43¢)

Position in π

The digit sequence 2040 first appears in π at position 17,677 of the decimal expansion (the 17,677ordinal-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 2040 on Pi Search ↗