Live analysis

3,840

3,840 is a composite number, even.

This number doesn't have a permanent NumberWiki page yet — what you see below is computed live. Pages get added to the permanent index when they're notable (years, primes, curated, etc.).

3,840 (three thousand eight hundred forty) is an even 4-digit number. It is a composite number with 36 divisors, and factors as 2⁸ × 3 × 5. Its proper divisors sum to 8,424, more than the number itself, making it an abundant number. Written other ways, in Roman numerals it is MMMDCCCXL and in binary, 111100000000.

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

Interestingness

★ ★ ★ ☆ ☆

5 notable facts · grade C

3,828 3,829 3,830 3,831 3,832 3,833 3,834 3,835 3,836 3,837 3,838 3,839 3,840 3,841 3,842 3,843 3,844 3,845 3,846 3,847 3,848 3,849 3,850 3,851 3,852

less more

Properties

Parity: Even
Digit count: 4
Digit sum: 15
Digit product: 0
Digital root: 6
Palindrome: No
Bit width: 12 bits
Reversed: 483
Recamán's sequence: a(6,248) = 3,840
Square (n²): 14,745,600
Cube (n³): 56,623,104,000
Divisor count: 36
σ(n) — sum of divisors: 12,264
φ(n) — Euler's totient: 1,024
Sum of prime factors: 24

Primality

Prime factorization: 2 ⁸ × 3 × 5

Nearest primes: 3,833 (−7) · 3,847 (+7)

Divisors & multiples

All divisors (36)

1 · 2 · 3 · 4 · 5 · 6 · 8 · 10 · 12 · 15 · 16 · 20 · 24 · 30 · 32 · 40 · 48 · 60 · 64 · 80 · 96 · 120 · 128 · 160 · 192 · 240 · 256 · 320 · 384 · 480 · 640 · 768 · 960 · 1280 · 1920 (half) · 3840

Aliquot sum (sum of proper divisors): 8,424

Factor pairs (a × b = 3,840)

1 × 3840

2 × 1920

3 × 1280

4 × 960

5 × 768

6 × 640

8 × 480

10 × 384

12 × 320

15 × 256

16 × 240

20 × 192

24 × 160

30 × 128

32 × 120

40 × 96

48 × 80

60 × 64

First multiples

3,840 · 7,680 (double) · 11,520 · 15,360 · 19,200 · 23,040 · 26,880 · 30,720 · 34,560 · 38,400

Sums & aliquot sequence

As consecutive integers: 1,279 + 1,280 + 1,281 766 + 767 + 768 + 769 + 770 249 + 250 + … + 263

Aliquot sequence: 3,840 → 8,424 → 16,986 → 19,014 → 19,026 → 28,398 → 28,410 → 39,846 → 42,954 → 42,966 → 76,842 → 94,038 → 121,002 → 166,230 → 266,202 → 336,582 → 446,778 — unresolved within range

Continued fraction of √n

√3,840 = [61; (1, 29, 1, 122)]

Period length 4 — the block in parentheses repeats forever.

Representations

In words: three thousand eight hundred forty
Ordinal: 3840th
Roman numeral: MMMDCCCXL
Binary: 111100000000
Octal: 7400
Hexadecimal: 0xF00
Base64: DwA=
One's complement: 61,695 (16-bit)
Scientific notation: 3.84 × 10³
As a duration: 3,840 s = 1 hour, 4 minutes

In other bases

ternary (3) 12021020

quaternary (4) 330000

quinary (5) 110330

senary (6) 25440

septenary (7) 14124

nonary (9) 5236

undecimal (11) 2981

duodecimal (12) 2280

tridecimal (13) 1995

tetradecimal (14) 1584

pentadecimal (15) 1210

As an angle

3,840° = 10 × 360° + 240°

240° ≈ 4.189 rad

Compass bearing: WSW (west-southwest)

Why does a circle have 360 degrees? →

Historical numeral systems

Babylonian (base 60): 𒁹 𒁹𒁹𒁹𒁹 ·
Egyptian hieroglyphic: 𓆼𓆼𓆼𓍢𓍢𓍢𓍢𓍢𓍢𓍢𓍢𓎆𓎆𓎆𓎆
Greek (Milesian): ͵γωμʹ
Mayan (base 20): 𝋩·𝋬·𝋠
Chinese: 三千八百四十
Chinese (financial): 參仟捌佰肆拾

In other modern scripts

Eastern Arabic ٣٨٤٠ Devanagari ३८४० Bengali ৩৮৪০ Tamil ௩௮௪௦ Thai ๓๘๔๐ Tibetan ༣༨༤༠ Khmer ៣៨៤០ Lao ໓໘໔໐ Burmese ၃၈၄၀

Digit at this position in famous constants

π — Pi (π): Digit 3,840 = 1
e — Euler's number (e): Digit 3,840 = 4
φ — Golden ratio (φ): Digit 3,840 = 4
√2 — Pythagoras's (√2): Digit 3,840 = 9
ln 2 — Natural log of 2: Digit 3,840 = 1
γ — Euler-Mascheroni (γ): Digit 3,840 = 2

Also seen as

Goldbach decomposition

Goldbach's conjecture says every even integer greater than 2 is the sum of two primes. For 3840, here are decompositions:

7 + 3833 = 3840
17 + 3823 = 3840
19 + 3821 = 3840
37 + 3803 = 3840
43 + 3797 = 3840
47 + 3793 = 3840
61 + 3779 = 3840
71 + 3769 = 3840

Showing the first eight; more decompositions exist.

Unicode codepoint

ༀ

Tibetan Syllable Om

U+0F00

Other letter (Lo)

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

Lookup U+0F00 on Compart ↗ Lookup on FileFormat.Info ↗

Hex color

#000F00

RGB(0, 15, 0)

IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.0.15.0.

Address: 0.0.15.0
Class: reserved
IPv4-mapped IPv6: ::ffff:0.0.15.0

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

Musical pitch

Heard as a frequency, 3,840 Hz is closest to:

Concert pitch (A4 = 440 Hz): B7 (3951.1 Hz, -49¢ — about midway to A♯7)
Scientific pitch (C4 = 256 Hz): B7 (3866.1 Hz, -12¢)
Baroque pitch (A4 = 415 Hz): C8 (3948.2 Hz, -48¢ — about midway to B7)

Position in π

The digit sequence 3840 first appears in π at position 3,229 of the decimal expansion (the 3,229ordinal-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 3840 on Pi Search ↗