Live analysis

13,380

13,380 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.).

13,380 (thirteen thousand three hundred eighty) is an even 5-digit number. It is a composite number with 24 divisors, and factors as 2² × 3 × 5 × 223. Its proper divisors sum to 24,252, more than the number itself, making it an abundant number. Written other ways, in hexadecimal, 0x3444.

Abundant Number Arithmetic Number Cube-Free Gapful Number Harshad / Niven Odious Number Pernicious Number Recamán's Sequence Semiperfect Number

Interestingness

★ ★ ★ ★ ☆

6 notable facts · grade B

13,368 13,369 13,370 13,371 13,372 13,373 13,374 13,375 13,376 13,377 13,378 13,379 13,380 13,381 13,382 13,383 13,384 13,385 13,386 13,387 13,388 13,389 13,390 13,391 13,392

less more

Properties

Parity: Even
Digit count: 5
Digit sum: 15
Digit product: 0
Digital root: 6
Palindrome: No
Bit width: 14 bits
Reversed: 8,331
Recamán's sequence: a(47,515) = 13,380
Square (n²): 179,024,400
Cube (n³): 2,395,346,472,000
Divisor count: 24
σ(n) — sum of divisors: 37,632
φ(n) — Euler's totient: 3,552
Sum of prime factors: 235

Primality

Prime factorization: 2 ² × 3 × 5 × 223

Nearest primes: 13,367 (−13) · 13,381 (+1)

Divisors & multiples

All divisors (24)

1 · 2 · 3 · 4 · 5 · 6 · 10 · 12 · 15 · 20 · 30 · 60 · 223 · 446 · 669 · 892 · 1115 · 1338 · 2230 · 2676 · 3345 · 4460 · 6690 (half) · 13380

Aliquot sum (sum of proper divisors): 24,252

Factor pairs (a × b = 13,380)

1 × 13380

2 × 6690

3 × 4460

4 × 3345

5 × 2676

6 × 2230

10 × 1338

12 × 1115

15 × 892

20 × 669

30 × 446

60 × 223

First multiples

13,380 · 26,760 (double) · 40,140 · 53,520 · 66,900 · 80,280 · 93,660 · 107,040 · 120,420 · 133,800

Sums & aliquot sequence

As consecutive integers: 4,459 + 4,460 + 4,461 2,674 + 2,675 + 2,676 + 2,677 + 2,678 1,669 + 1,670 + … + 1,676 885 + 886 + … + 899

Aliquot sequence: 13,380 → 24,252 → 34,884 → 65,916 → 100,796 → 77,956 → 58,474 → 37,052 → 29,308 → 25,124 → 22,924 → 20,924 → 15,700 → 18,586 → 9,296 → 11,536 → 14,256 — unresolved within range

Continued fraction of √n

√13,380 = [115; (1, 2, 20, 1, 2, 3, 3, 1, 1, 1, 1, 1, 3, 1, 10, 1, 3, 1, 1, 1, 1, 1, 3, 3, …)]

Period length 30 — the block in parentheses repeats forever.

Representations

In words: thirteen thousand three hundred eighty
Ordinal: 13380th
Binary: 11010001000100
Octal: 32104
Hexadecimal: 0x3444
Base64: NEQ=
One's complement: 52,155 (16-bit)
Scientific notation: 1.338 × 10⁴
As a duration: 13,380 s = 3 hours, 43 minutes

In other bases

ternary (3) 200100120

quaternary (4) 3101010

quinary (5) 412010

senary (6) 141540

septenary (7) 54003

nonary (9) 20316

undecimal (11) a064

duodecimal (12) 78b0

tridecimal (13) 6123

tetradecimal (14) 4c3a

pentadecimal (15) 3e70

As an angle

13,380° = 37 × 360° + 60°

60° ≈ 1.047 rad

Compass bearing: ENE (east-northeast)

Why does a circle have 360 degrees? →

Historical numeral systems

Babylonian (base 60): 𒁹𒁹𒁹 𒌋𒌋𒌋𒌋𒁹𒁹𒁹 ·
Egyptian hieroglyphic: 𓂍𓆼𓆼𓆼𓍢𓍢𓍢𓎆𓎆𓎆𓎆𓎆𓎆𓎆𓎆
Greek (Milesian): ͵ιγτπʹ
Mayan (base 20): 𝋡·𝋭·𝋩·𝋠
Chinese: 一萬三千三百八十
Chinese (financial): 壹萬參仟參佰捌拾

In other modern scripts

Eastern Arabic ١٣٣٨٠ Devanagari १३३८० Bengali ১৩৩৮০ Tamil ௧௩௩௮௦ Thai ๑๓๓๘๐ Tibetan ༡༣༣༨༠ Khmer ១៣៣៨០ Lao ໑໓໓໘໐ Burmese ၁၃၃၈၀

Digit at this position in famous constants

π — Pi (π): Digit 13,380 = 1
e — Euler's number (e): Digit 13,380 = 5
φ — Golden ratio (φ): Digit 13,380 = 3
√2 — Pythagoras's (√2): Digit 13,380 = 6
ln 2 — Natural log of 2: Digit 13,380 = 8
γ — Euler-Mascheroni (γ): Digit 13,380 = 7

Also seen as

Goldbach decomposition

Goldbach's conjecture says every even integer greater than 2 is the sum of two primes. For 13380, here are decompositions:

13 + 13367 = 13380
41 + 13339 = 13380
43 + 13337 = 13380
53 + 13327 = 13380
67 + 13313 = 13380
71 + 13309 = 13380
83 + 13297 = 13380
89 + 13291 = 13380

Showing the first eight; more decompositions exist.

Unicode codepoint

㑄

CJK Unified Ideograph-3444

U+3444

Other letter (Lo)

UTF-8 encoding: E3 91 84 (3 bytes).

Lookup U+3444 on Compart ↗ Lookup on FileFormat.Info ↗

Hex color

#003444

RGB(0, 52, 68)

IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.0.52.68.

Address: 0.0.52.68
Class: reserved
IPv4-mapped IPv6: ::ffff:0.0.52.68

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

Musical pitch

Heard as a frequency, 13,380 Hz is closest to:

Concert pitch (A4 = 440 Hz): G♯9 (13289.8 Hz, +12¢)
Scientific pitch (C4 = 256 Hz): G♯9 (13004 Hz, +49¢ — about midway to A9)
Baroque pitch (A4 = 415 Hz): A9 (13280 Hz, +13¢)

Position in π

The digit sequence 13380 first appears in π at position 24,143 of the decimal expansion (the 24,143ordinal-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 13380 on Pi Search ↗