Live analysis

13,800

13,800 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.).

13,800 (thirteen thousand eight hundred) is an even 5-digit number. It is a composite number with 48 divisors, and factors as 2³ × 3 × 5² × 23. Its proper divisors sum to 30,840, more than the number itself, making it an abundant number. Written other ways, in hexadecimal, 0x35E8.

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

Interestingness

★ ★ ★ ★ ☆

6 notable facts · grade B

13,788 13,789 13,790 13,791 13,792 13,793 13,794 13,795 13,796 13,797 13,798 13,799 13,800 13,801 13,802 13,803 13,804 13,805 13,806 13,807 13,808 13,809 13,810 13,811 13,812

less more

Properties

Parity: Even
Digit count: 5
Digit sum: 12
Digit product: 0
Digital root: 3
Palindrome: No
Bit width: 14 bits
Reversed: 831
Recamán's sequence: a(21,116) = 13,800
Square (n²): 190,440,000
Cube (n³): 2,628,072,000,000
Divisor count: 48
σ(n) — sum of divisors: 44,640
φ(n) — Euler's totient: 3,520
Sum of prime factors: 42

Primality

Prime factorization: 2 ³ × 3 × 5 ² × 23

Nearest primes: 13,799 (−1) · 13,807 (+7)

Divisors & multiples

All divisors (48)

1 · 2 · 3 · 4 · 5 · 6 · 8 · 10 · 12 · 15 · 20 · 23 · 24 · 25 · 30 · 40 · 46 · 50 · 60 · 69 · 75 · 92 · 100 · 115 · 120 · 138 · 150 · 184 · 200 · 230 · 276 · 300 · 345 · 460 · 552 · 575 · 600 · 690 · 920 · 1150 · 1380 · 1725 · 2300 · 2760 · 3450 · 4600 · 6900 (half) · 13800

Aliquot sum (sum of proper divisors): 30,840

Factor pairs (a × b = 13,800)

1 × 13800

2 × 6900

3 × 4600

4 × 3450

5 × 2760

6 × 2300

8 × 1725

10 × 1380

12 × 1150

15 × 920

20 × 690

23 × 600

24 × 575

25 × 552

30 × 460

40 × 345

46 × 300

50 × 276

60 × 230

69 × 200

75 × 184

92 × 150

100 × 138

115 × 120

First multiples

13,800 · 27,600 (double) · 41,400 · 55,200 · 69,000 · 82,800 · 96,600 · 110,400 · 124,200 · 138,000

Sums & aliquot sequence

As consecutive integers: 4,599 + 4,600 + 4,601 2,758 + 2,759 + 2,760 + 2,761 + 2,762 913 + 914 + … + 927 855 + 856 + … + 870

Aliquot sequence: 13,800 → 30,840 → 62,040 → 145,320 → 355,800 → 749,040 → 1,573,728 → 2,945,640 → 5,891,640 → 12,403,560 → 27,674,520 → 61,628,520 → 124,111,320 → 258,299,400 → 542,430,600 → 1,155,942,840 → 2,578,646,760 — unresolved within range

Continued fraction of √n

√13,800 = [117; (2, 8, 1, 8, 1, 8, 2, 234)]

Period length 8 — the block in parentheses repeats forever.

Representations

In words: thirteen thousand eight hundred
Ordinal: 13800th
Binary: 11010111101000
Octal: 32750
Hexadecimal: 0x35E8
Base64: Neg=
One's complement: 51,735 (16-bit)
Scientific notation: 1.38 × 10⁴
As a duration: 13,800 s = 3 hours, 50 minutes

In other bases

ternary (3) 200221010

quaternary (4) 3113220

quinary (5) 420200

senary (6) 143520

septenary (7) 55143

nonary (9) 20833

undecimal (11) a406

duodecimal (12) 7ba0

tridecimal (13) 6387

tetradecimal (14) 505a

pentadecimal (15) 4150

As an angle

13,800° = 38 × 360° + 120°

120° ≈ 2.094 rad

Compass bearing: ESE (east-southeast)

Why does a circle have 360 degrees? →

Historical numeral systems

Babylonian (base 60): 𒁹𒁹𒁹 𒌋𒌋𒌋𒌋𒌋 ·
Egyptian hieroglyphic: 𓂍𓆼𓆼𓆼𓍢𓍢𓍢𓍢𓍢𓍢𓍢𓍢
Greek (Milesian): ͵ιγωʹ
Mayan (base 20): 𝋡·𝋮·𝋪·𝋠
Chinese: 一萬三千八百
Chinese (financial): 壹萬參仟捌佰

In other modern scripts

Eastern Arabic ١٣٨٠٠ Devanagari १३८०० Bengali ১৩৮০০ Tamil ௧௩௮௦௦ Thai ๑๓๘๐๐ Tibetan ༡༣༨༠༠ Khmer ១៣៨០០ Lao ໑໓໘໐໐ Burmese ၁၃၈၀၀

Digit at this position in famous constants

π — Pi (π): Digit 13,800 = 6
e — Euler's number (e): Digit 13,800 = 1
φ — Golden ratio (φ): Digit 13,800 = 2
√2 — Pythagoras's (√2): Digit 13,800 = 8
ln 2 — Natural log of 2: Digit 13,800 = 2
γ — Euler-Mascheroni (γ): Digit 13,800 = 3

Also seen as

Goldbach decomposition

Goldbach's conjecture says every even integer greater than 2 is the sum of two primes. For 13800, here are decompositions:

11 + 13789 = 13800
19 + 13781 = 13800
37 + 13763 = 13800
41 + 13759 = 13800
43 + 13757 = 13800
71 + 13729 = 13800
79 + 13721 = 13800
89 + 13711 = 13800

Showing the first eight; more decompositions exist.

Unicode codepoint

㗨

CJK Unified Ideograph-35E8

U+35E8

Other letter (Lo)

UTF-8 encoding: E3 97 A8 (3 bytes).

Lookup U+35E8 on Compart ↗ Lookup on FileFormat.Info ↗

Hex color

#0035E8

RGB(0, 53, 232)

IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.0.53.232.

Address: 0.0.53.232
Class: reserved
IPv4-mapped IPv6: ::ffff:0.0.53.232

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

Musical pitch

Heard as a frequency, 13,800 Hz is closest to:

Concert pitch (A4 = 440 Hz): A9 (14080 Hz, -35¢)
Scientific pitch (C4 = 256 Hz): A9 (13777.2 Hz, +3¢)
Baroque pitch (A4 = 415 Hz): A♯9 (14069.7 Hz, -34¢)

Position in π

The digit sequence 13800 first appears in π at position 109,132 of the decimal expansion (the 109,132ordinal-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 13800 on Pi Search ↗