Live analysis

13,020

13,020 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.).

13,020 (thirteen thousand twenty) is an even 5-digit number. It is a composite number with 48 divisors, and factors as 2² × 3 × 5 × 7 × 31. Its proper divisors sum to 29,988, more than the number itself, making it an abundant number. Written other ways, in hexadecimal, 0x32DC.

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

Interestingness

★ ★ ★ ★ ☆

7 notable facts · grade B

13,008 13,009 13,010 13,011 13,012 13,013 13,014 13,015 13,016 13,017 13,018 13,019 13,020 13,021 13,022 13,023 13,024 13,025 13,026 13,027 13,028 13,029 13,030 13,031 13,032

less more

Properties

Parity: Even
Digit count: 5
Digit sum: 6
Digit product: 0
Digital root: 6
Palindrome: No
Bit width: 14 bits
Reversed: 2,031
Recamán's sequence: a(48,235) = 13,020
Square (n²): 169,520,400
Cube (n³): 2,207,155,608,000
Divisor count: 48
σ(n) — sum of divisors: 43,008
φ(n) — Euler's totient: 2,880
Sum of prime factors: 50

Primality

Prime factorization: 2 ² × 3 × 5 × 7 × 31

Nearest primes: 13,009 (−11) · 13,033 (+13)

Divisors & multiples

All divisors (48)

1 · 2 · 3 · 4 · 5 · 6 · 7 · 10 · 12 · 14 · 15 · 20 · 21 · 28 · 30 · 31 · 35 · 42 · 60 · 62 · 70 · 84 · 93 · 105 · 124 · 140 · 155 · 186 · 210 · 217 · 310 · 372 · 420 · 434 · 465 · 620 · 651 · 868 · 930 · 1085 · 1302 · 1860 · 2170 · 2604 · 3255 · 4340 · 6510 (half) · 13020

Aliquot sum (sum of proper divisors): 29,988

Factor pairs (a × b = 13,020)

1 × 13020

2 × 6510

3 × 4340

4 × 3255

5 × 2604

6 × 2170

7 × 1860

10 × 1302

12 × 1085

14 × 930

15 × 868

20 × 651

21 × 620

28 × 465

30 × 434

31 × 420

35 × 372

42 × 310

60 × 217

62 × 210

70 × 186

84 × 155

93 × 140

105 × 124

First multiples

13,020 · 26,040 (double) · 39,060 · 52,080 · 65,100 · 78,120 · 91,140 · 104,160 · 117,180 · 130,200

Sums & aliquot sequence

As consecutive integers: 4,339 + 4,340 + 4,341 2,602 + 2,603 + 2,604 + 2,605 + 2,606 1,857 + 1,858 + … + 1,863 1,624 + 1,625 + … + 1,631

Aliquot sequence: 13,020 → 29,988 → 63,378 → 93,870 → 186,930 → 322,254 → 376,002 → 547,470 → 1,249,650 → 2,108,952 → 3,942,288 → 8,670,000 → 21,061,108 → 15,795,838 → 7,915,850 → 7,285,558 → 5,607,626 — unresolved within range

Continued fraction of √n

√13,020 = [114; (9, 1, 1, 56, 1, 1, 9, 228)]

Period length 8 — the block in parentheses repeats forever.

Representations

In words: thirteen thousand twenty
Ordinal: 13020th
Binary: 11001011011100
Octal: 31334
Hexadecimal: 0x32DC
Base64: Mtw=
One's complement: 52,515 (16-bit)
Scientific notation: 1.302 × 10⁴
As a duration: 13,020 s = 3 hours, 37 minutes

In other bases

ternary (3) 122212020

quaternary (4) 3023130

quinary (5) 404040

senary (6) 140140

septenary (7) 52650

nonary (9) 18766

undecimal (11) 9867

duodecimal (12) 7650

tridecimal (13) 5c07

tetradecimal (14) 4a60

pentadecimal (15) 3cd0

As an angle

13,020° = 36 × 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 𒌋𒌋𒌋𒁹𒁹𒁹𒁹𒁹𒁹𒁹 ·
Egyptian hieroglyphic: 𓂍𓆼𓆼𓆼𓎆𓎆
Greek (Milesian): ͵ιγκʹ
Mayan (base 20): 𝋡·𝋬·𝋫·𝋠
Chinese: 一萬三千零二十
Chinese (financial): 壹萬參仟零貳拾

In other modern scripts

Eastern Arabic ١٣٠٢٠ Devanagari १३०२० Bengali ১৩০২০ Tamil ௧௩௦௨௦ Thai ๑๓๐๒๐ Tibetan ༡༣༠༢༠ Khmer ១៣០២០ Lao ໑໓໐໒໐ Burmese ၁၃၀၂၀

Digit at this position in famous constants

π — Pi (π): Digit 13,020 = 9
e — Euler's number (e): Digit 13,020 = 6
φ — Golden ratio (φ): Digit 13,020 = 6
√2 — Pythagoras's (√2): Digit 13,020 = 9
ln 2 — Natural log of 2: Digit 13,020 = 0
γ — Euler-Mascheroni (γ): Digit 13,020 = 9

Also seen as

Goldbach decomposition

Goldbach's conjecture says every even integer greater than 2 is the sum of two primes. For 13020, here are decompositions:

11 + 13009 = 13020
13 + 13007 = 13020
17 + 13003 = 13020
19 + 13001 = 13020
37 + 12983 = 13020
41 + 12979 = 13020
47 + 12973 = 13020
53 + 12967 = 13020

Showing the first eight; more decompositions exist.

Unicode codepoint

㋜

Circled Katakana Su

U+32DC

Other symbol (So)

UTF-8 encoding: E3 8B 9C (3 bytes).

Lookup U+32DC on Compart ↗ Lookup on FileFormat.Info ↗

Hex color

#0032DC

RGB(0, 50, 220)

IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.0.50.220.

Address: 0.0.50.220
Class: reserved
IPv4-mapped IPv6: ::ffff:0.0.50.220

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

Musical pitch

Heard as a frequency, 13,020 Hz is closest to:

Concert pitch (A4 = 440 Hz): G♯9 (13289.8 Hz, -36¢)
Scientific pitch (C4 = 256 Hz): G♯9 (13004 Hz, +2¢)
Baroque pitch (A4 = 415 Hz): A9 (13280 Hz, -34¢)

Position in π

The digit sequence 13020 first appears in π at position 3,828 of the decimal expansion (the 3,828ordinal-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 13020 on Pi Search ↗