Live analysis

13,920

13,920 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.).

13,920 (thirteen thousand nine hundred twenty) is an even 5-digit number. It is a composite number with 48 divisors, and factors as 2⁵ × 3 × 5 × 29. Its proper divisors sum to 31,440, more than the number itself, making it an abundant number. Written other ways, in hexadecimal, 0x3660.

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

Interestingness

★ ★ ★ ★ ★

8 notable facts · grade A

13,908 13,909 13,910 13,911 13,912 13,913 13,914 13,915 13,916 13,917 13,918 13,919 13,920 13,921 13,922 13,923 13,924 13,925 13,926 13,927 13,928 13,929 13,930 13,931 13,932

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Properties

Parity: Even
Digit count: 5
Digit sum: 15
Digit product: 0
Digital root: 6
Palindrome: No
Bit width: 14 bits
Reversed: 2,931
Recamán's sequence: a(20,876) = 13,920
Square (n²): 193,766,400
Cube (n³): 2,697,228,288,000
Divisor count: 48
σ(n) — sum of divisors: 45,360
φ(n) — Euler's totient: 3,584
Sum of prime factors: 47

Primality

Prime factorization: 2 ⁵ × 3 × 5 × 29

Nearest primes: 13,913 (−7) · 13,921 (+1)

Divisors & multiples

All divisors (48)

1 · 2 · 3 · 4 · 5 · 6 · 8 · 10 · 12 · 15 · 16 · 20 · 24 · 29 · 30 · 32 · 40 · 48 · 58 · 60 · 80 · 87 · 96 · 116 · 120 · 145 · 160 · 174 · 232 · 240 · 290 · 348 · 435 · 464 · 480 · 580 · 696 · 870 · 928 · 1160 · 1392 · 1740 · 2320 · 2784 · 3480 · 4640 · 6960 (half) · 13920

Aliquot sum (sum of proper divisors): 31,440

Factor pairs (a × b = 13,920)

1 × 13920

2 × 6960

3 × 4640

4 × 3480

5 × 2784

6 × 2320

8 × 1740

10 × 1392

12 × 1160

15 × 928

16 × 870

20 × 696

24 × 580

29 × 480

30 × 464

32 × 435

40 × 348

48 × 290

58 × 240

60 × 232

80 × 174

87 × 160

96 × 145

116 × 120

First multiples

13,920 · 27,840 (double) · 41,760 · 55,680 · 69,600 · 83,520 · 97,440 · 111,360 · 125,280 · 139,200

Sums & aliquot sequence

As consecutive integers: 4,639 + 4,640 + 4,641 2,782 + 2,783 + 2,784 + 2,785 + 2,786 921 + 922 + … + 935 466 + 467 + … + 494

Aliquot sequence: 13,920 → 31,440 → 66,768 → 120,720 → 254,256 → 402,696 → 945,144 → 1,614,816 → 3,873,744 → 9,382,290 → 13,135,278 → 15,766,098 → 16,301,262 → 16,352,898 → 17,432,958 → 18,175,362 → 22,682,238 — unresolved within range

Continued fraction of √n

√13,920 = [117; (1, 57, 1, 234)]

Period length 4 — the block in parentheses repeats forever.

Representations

In words: thirteen thousand nine hundred twenty
Ordinal: 13920th
Binary: 11011001100000
Octal: 33140
Hexadecimal: 0x3660
Base64: NmA=
One's complement: 51,615 (16-bit)
Scientific notation: 1.392 × 10⁴
As a duration: 13,920 s = 3 hours, 52 minutes

In other bases

ternary (3) 201002120

quaternary (4) 3121200

quinary (5) 421140

senary (6) 144240

septenary (7) 55404

nonary (9) 21076

undecimal (11) a505

duodecimal (12) 8080

tridecimal (13) 644a

tetradecimal (14) 5104

pentadecimal (15) 41d0

As an angle

13,920° = 38 × 360° + 240°

240° ≈ 4.189 rad

Compass bearing: WSW (west-southwest)

Why does a circle have 360 degrees? →

Historical numeral systems

Babylonian (base 60): 𒁹𒁹𒁹 𒌋𒌋𒌋𒌋𒌋𒁹𒁹 ·
Egyptian hieroglyphic: 𓂍𓆼𓆼𓆼𓍢𓍢𓍢𓍢𓍢𓍢𓍢𓍢𓍢𓎆𓎆
Greek (Milesian): ͵ιγϡκʹ
Mayan (base 20): 𝋡·𝋮·𝋰·𝋠
Chinese: 一萬三千九百二十
Chinese (financial): 壹萬參仟玖佰貳拾

In other modern scripts

Eastern Arabic ١٣٩٢٠ Devanagari १३९२० Bengali ১৩৯২০ Tamil ௧௩௯௨௦ Thai ๑๓๙๒๐ Tibetan ༡༣༩༢༠ Khmer ១៣៩២០ Lao ໑໓໙໒໐ Burmese ၁၃၉၂၀

Digit at this position in famous constants

π — Pi (π): Digit 13,920 = 8
e — Euler's number (e): Digit 13,920 = 2
φ — Golden ratio (φ): Digit 13,920 = 4
√2 — Pythagoras's (√2): Digit 13,920 = 0
ln 2 — Natural log of 2: Digit 13,920 = 9
γ — Euler-Mascheroni (γ): Digit 13,920 = 5

Also seen as

Goldbach decomposition

Goldbach's conjecture says every even integer greater than 2 is the sum of two primes. For 13920, here are decompositions:

7 + 13913 = 13920
13 + 13907 = 13920
17 + 13903 = 13920
19 + 13901 = 13920
37 + 13883 = 13920
41 + 13879 = 13920
43 + 13877 = 13920
47 + 13873 = 13920

Showing the first eight; more decompositions exist.

Unicode codepoint

㙠

CJK Unified Ideograph-3660

U+3660

Other letter (Lo)

UTF-8 encoding: E3 99 A0 (3 bytes).

Lookup U+3660 on Compart ↗ Lookup on FileFormat.Info ↗

Hex color

#003660

RGB(0, 54, 96)

IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.0.54.96.

Address: 0.0.54.96
Class: reserved
IPv4-mapped IPv6: ::ffff:0.0.54.96

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

Musical pitch

Heard as a frequency, 13,920 Hz is closest to:

Concert pitch (A4 = 440 Hz): A9 (14080 Hz, -20¢)
Scientific pitch (C4 = 256 Hz): A9 (13777.2 Hz, +18¢)
Baroque pitch (A4 = 415 Hz): A♯9 (14069.7 Hz, -19¢)

Position in π

The digit sequence 13920 first appears in π at position 43,063 of the decimal expansion (the 43,063ordinal-suffix:rd 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 13920 on Pi Search ↗