Live analysis

13,140

13,140 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.).

13,140 (thirteen thousand one hundred forty) is an even 5-digit number. It is a composite number with 36 divisors, and factors as 2² × 3² × 5 × 73. Its proper divisors sum to 27,264, more than the number itself, making it an abundant number. Written other ways, in hexadecimal, 0x3354.

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

Interestingness

★ ★ ★ ★ ☆

7 notable facts · grade B

13,128 13,129 13,130 13,131 13,132 13,133 13,134 13,135 13,136 13,137 13,138 13,139 13,140 13,141 13,142 13,143 13,144 13,145 13,146 13,147 13,148 13,149 13,150 13,151 13,152

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Properties

Parity: Even
Digit count: 5
Digit sum: 9
Digit product: 0
Digital root: 9
Palindrome: No
Bit width: 14 bits
Reversed: 4,131
Recamán's sequence: a(47,995) = 13,140
Square (n²): 172,659,600
Cube (n³): 2,268,747,144,000
Divisor count: 36
σ(n) — sum of divisors: 40,404
φ(n) — Euler's totient: 3,456
Sum of prime factors: 88

Primality

Prime factorization: 2 ² × 3 ² × 5 × 73

Nearest primes: 13,127 (−13) · 13,147 (+7)

Divisors & multiples

All divisors (36)

1 · 2 · 3 · 4 · 5 · 6 · 9 · 10 · 12 · 15 · 18 · 20 · 30 · 36 · 45 · 60 · 73 · 90 · 146 · 180 · 219 · 292 · 365 · 438 · 657 · 730 · 876 · 1095 · 1314 · 1460 · 2190 · 2628 · 3285 · 4380 · 6570 (half) · 13140

Aliquot sum (sum of proper divisors): 27,264

Factor pairs (a × b = 13,140)

1 × 13140

2 × 6570

3 × 4380

4 × 3285

5 × 2628

6 × 2190

9 × 1460

10 × 1314

12 × 1095

15 × 876

18 × 730

20 × 657

30 × 438

36 × 365

45 × 292

60 × 219

73 × 180

90 × 146

First multiples

13,140 · 26,280 (double) · 39,420 · 52,560 · 65,700 · 78,840 · 91,980 · 105,120 · 118,260 · 131,400

Sums & aliquot sequence

As a sum of two squares: 12² + 114² = 78² + 84²

As consecutive integers: 4,379 + 4,380 + 4,381 2,626 + 2,627 + 2,628 + 2,629 + 2,630 1,639 + 1,640 + … + 1,646 1,456 + 1,457 + … + 1,464

Aliquot sequence: 13,140 → 27,264 → 46,176 → 87,888 → 139,280 → 184,732 → 138,556 → 135,620 → 149,224 → 143,096 → 134,344 → 153,656 → 134,464 → 158,144 → 201,520 → 311,840 → 425,260 — unresolved within range

Continued fraction of √n

√13,140 = [114; (1, 1, 1, 2, 2, 1, 5, 1, 5, 1, 1, 13, 1, 3, 1, 2, 1, 24, 1, 2, 1, 3, 1, 13, …)]

Period length 36 — the block in parentheses repeats forever.

Representations

In words: thirteen thousand one hundred forty
Ordinal: 13140th
Binary: 11001101010100
Octal: 31524
Hexadecimal: 0x3354
Base64: M1Q=
One's complement: 52,395 (16-bit)
Scientific notation: 1.314 × 10⁴
As a duration: 13,140 s = 3 hours, 39 minutes

In other bases

ternary (3) 200000200

quaternary (4) 3031110

quinary (5) 410030

senary (6) 140500

septenary (7) 53211

nonary (9) 20020

undecimal (11) 9966

duodecimal (12) 7730

tridecimal (13) 5c9a

tetradecimal (14) 4b08

pentadecimal (15) 3d60

As an angle

13,140° = 36 × 360° + 180°

180° ≈ 3.142 rad

Compass bearing: S (south)

Why does a circle have 360 degrees? →

Historical numeral systems

Babylonian (base 60): 𒁹𒁹𒁹 𒌋𒌋𒌋𒁹𒁹𒁹𒁹𒁹𒁹𒁹𒁹𒁹 ·
Egyptian hieroglyphic: 𓂍𓆼𓆼𓆼𓍢𓎆𓎆𓎆𓎆
Greek (Milesian): ͵ιγρμʹ
Mayan (base 20): 𝋡·𝋬·𝋱·𝋠
Chinese: 一萬三千一百四十
Chinese (financial): 壹萬參仟壹佰肆拾

In other modern scripts

Eastern Arabic ١٣١٤٠ Devanagari १३१४० Bengali ১৩১৪০ Tamil ௧௩௧௪௦ Thai ๑๓๑๔๐ Tibetan ༡༣༡༤༠ Khmer ១៣១៤០ Lao ໑໓໑໔໐ Burmese ၁၃၁၄၀

Digit at this position in famous constants

π — Pi (π): Digit 13,140 = 3
e — Euler's number (e): Digit 13,140 = 4
φ — Golden ratio (φ): Digit 13,140 = 8
√2 — Pythagoras's (√2): Digit 13,140 = 6
ln 2 — Natural log of 2: Digit 13,140 = 1
γ — Euler-Mascheroni (γ): Digit 13,140 = 5

Also seen as

Goldbach decomposition

Goldbach's conjecture says every even integer greater than 2 is the sum of two primes. For 13140, here are decompositions:

13 + 13127 = 13140
19 + 13121 = 13140
31 + 13109 = 13140
37 + 13103 = 13140
41 + 13099 = 13140
47 + 13093 = 13140
97 + 13043 = 13140
103 + 13037 = 13140

Showing the first eight; more decompositions exist.

Unicode codepoint

㍔

Square Ruuburu

U+3354

Other symbol (So)

UTF-8 encoding: E3 8D 94 (3 bytes).

Lookup U+3354 on Compart ↗ Lookup on FileFormat.Info ↗

Hex color

#003354

RGB(0, 51, 84)

IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.0.51.84.

Address: 0.0.51.84
Class: reserved
IPv4-mapped IPv6: ::ffff:0.0.51.84

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

Musical pitch

Heard as a frequency, 13,140 Hz is closest to:

Concert pitch (A4 = 440 Hz): G♯9 (13289.8 Hz, -20¢)
Scientific pitch (C4 = 256 Hz): G♯9 (13004 Hz, +18¢)
Baroque pitch (A4 = 415 Hz): A9 (13280 Hz, -18¢)

Position in π

The digit sequence 13140 first appears in π at position 4,245 of the decimal expansion (the 4,245ordinal-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 13140 on Pi Search ↗