Number

2,048

2,048 is a composite number, even, a calendar year.

2,048 (two thousand forty-eight) is an even 4-digit number. It is a composite number with 12 divisors, and factors as 2¹¹. It is a power of two (2¹¹). Written other ways, in Roman numerals it is MMXLVIII and in binary, 100000000000.

Cake Number Deficient Number Frugal Number Odious Number Power of Two Powerful Number Practical Number Recamán's Sequence Year

Interestingness

★ ★ ★ ★ ☆

6 notable facts · grade B

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 2,053 2,054 2,055 2,056 2,057 2,058 2,059 2,060

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Historical context — 2048 AD

Topics referred to by the same term

2048 may refer to:AD 2048, a year in the 2040s 2048 (number) 2048 , a puzzle game 2048: Nowhere to Run, a 2017 American science-fiction film

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: 53
Long year: contains 53 ISO weeks.
Started on: Wednesday
January 1, 2048
Ended on: Thursday
December 31, 2048
Friday the 13ths: 2
2 Friday the 13ths this year.
Easter Sunday: April 5
Sunday, April 5, 2048
Decade: 2040s
2040–2049
Century: 21st century
2001–2100
Millennium: 3rd millennium
2001–3000
Years until: 22
22 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: 5808 / 5809 AM
Rosh Hashanah falls in September/October.
Islamic Hijri: 1470 / 1471 AH
Lunar calendar; year spans differ from Gregorian.
Chinese: Year of the zodiac:Earth zodiac:Dragon
Sexagenary cycle position 5 of 60. Lunar new year falls in late January / mid-February.
Buddhist Era: 2591 BE
Counted from the parinirvana of the Buddha (Theravada / Thai / Sri Lankan convention).
Persian Solar Hijri: 1426 / 1427 SH
Iranian calendar; Nowruz (new year) falls on the spring equinox.
Ethiopian: 2040 / 2041 ET
Year boundary at Enkutatash (September 11/12).
Indian National (Saka): 1970 / 1969 Saka
Indian national calendar; year starts in March.
Japanese: Reiwa 30
Reign-era counting from the start of each emperor's reign.

Properties

Parity: Even
Digit count: 4
Digit sum: 14
Digit product: 0
Digital root: 5
Palindrome: No
Bit width: 12 bits
Reversed: 8,402
Recamán's sequence: a(3,655) = 2,048
Square (n²): 4,194,304
Cube (n³): 8,589,934,592
Divisor count: 12
σ(n) — sum of divisors: 4,095
φ(n) — Euler's totient: 1,024
Sum of prime factors: 22

Primality

Prime factorization: 2 ¹¹

Nearest primes: 2,039 (−9) · 2,053 (+5)

Divisors & multiples

All divisors (12)

1 · 2 · 4 · 8 · 16 · 32 · 64 · 128 · 256 · 512 · 1024 (half) · 2048

Aliquot sum (sum of proper divisors): 2,047

Factor pairs (a × b = 2,048)

1 × 2048

2 × 1024

4 × 512

8 × 256

16 × 128

32 × 64

First multiples

2,048 · 4,096 (double) · 6,144 · 8,192 · 10,240 · 12,288 · 14,336 · 16,384 · 18,432 · 20,480

Sums & aliquot sequence

As a sum of two squares: 32² + 32²

Aliquot sequence: 2,048 → 2,047 → 113 → 1 → 0 — terminates at zero

Continued fraction of √n

√2,048 = [45; (3, 1, 12, 5, 1, 1, 2, 1, 2, 4, 1, 21, 1, 4, 2, 1, 2, 1, 1, 5, 12, 1, 3, 90)]

Period length 24 — the block in parentheses repeats forever.

Representations

In words: two thousand forty-eight
Ordinal: 2048th
Roman numeral: MMXLVIII
Binary: 100000000000
Octal: 4000
Hexadecimal: 0x800
Base64: CAA=
One's complement: 63,487 (16-bit)
Scientific notation: 2.048 × 10³
As a duration: 2,048 s = 34 minutes, 8 seconds

In other bases

ternary (3) 2210212

quaternary (4) 200000

quinary (5) 31143

senary (6) 13252

septenary (7) 5654

nonary (9) 2725

undecimal (11) 15a2

duodecimal (12) 1228

tridecimal (13) c17

tetradecimal (14) a64

pentadecimal (15) 918

As an angle

2,048° = 5 × 360° + 248°

248° ≈ 4.328 rad

Compass bearing: WSW (west-southwest)

Why does a circle have 360 degrees? →

Historical numeral systems

Babylonian (base 60): 𒌋𒌋𒌋𒁹𒁹𒁹𒁹 𒁹𒁹𒁹𒁹𒁹𒁹𒁹𒁹
Egyptian hieroglyphic: 𓆼𓆼𓎆𓎆𓎆𓎆𓏺𓏺𓏺𓏺𓏺𓏺𓏺𓏺
Greek (Milesian): ͵βμηʹ
Mayan (base 20): 𝋥·𝋢·𝋨
Chinese: 二千零四十八
Chinese (financial): 貳仟零肆拾捌

In other modern scripts

Eastern Arabic ٢٠٤٨ Devanagari २०४८ Bengali ২০৪৮ Tamil ௨௦௪௮ Thai ๒๐๔๘ Tibetan ༢༠༤༨ Khmer ២០៤៨ Lao ໒໐໔໘ Burmese ၂၀၄၈

Digit at this position in famous constants

π — Pi (π): Digit 2,048 = 4
e — Euler's number (e): Digit 2,048 = 3
φ — Golden ratio (φ): Digit 2,048 = 6
√2 — Pythagoras's (√2): Digit 2,048 = 7
ln 2 — Natural log of 2: Digit 2,048 = 1
γ — Euler-Mascheroni (γ): Digit 2,048 = 9

Also seen as

Goldbach decomposition

Goldbach's conjecture says every even integer greater than 2 is the sum of two primes. For 2048, here are decompositions:

19 + 2029 = 2048
31 + 2017 = 2048
37 + 2011 = 2048
61 + 1987 = 2048
97 + 1951 = 2048
181 + 1867 = 2048
271 + 1777 = 2048
307 + 1741 = 2048

Showing the first eight; more decompositions exist.

Unicode codepoint

ࠀ

Samaritan Letter Alaf

U+0800

Other letter (Lo)

UTF-8 encoding: E0 A0 80 (3 bytes).

Lookup U+0800 on Compart ↗ Lookup on FileFormat.Info ↗

Hex color

#000800

RGB(0, 8, 0)

IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.0.8.0.

Address: 0.0.8.0
Class: reserved
IPv4-mapped IPv6: ::ffff:0.0.8.0

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

Musical pitch

Heard as a frequency, 2,048 Hz is closest to:

Concert pitch (A4 = 440 Hz): C7 (2093 Hz, -38¢)
Scientific pitch (C4 = 256 Hz): C7 (2048 Hz, exact)
Baroque pitch (A4 = 415 Hz): C♯7 (2091.5 Hz, -36¢)

Position in π

The digit sequence 2048 first appears in π at position 26,862 of the decimal expansion (the 26,862ordinal-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 2048 on Pi Search ↗