Live analysis

13,000

13,000 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.).

13,000 (thirteen thousand) is an even 5-digit number. It is a composite number with 32 divisors, and factors as 2³ × 5³ × 13. Its proper divisors sum to 19,760, more than the number itself, making it an abundant number. Written other ways, in hexadecimal, 0x32C8.

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

Interestingness

★ ★ ★ ★ ☆

7 notable facts · grade B

12,988 12,989 12,990 12,991 12,992 12,993 12,994 12,995 12,996 12,997 12,998 12,999 13,000 13,001 13,002 13,003 13,004 13,005 13,006 13,007 13,008 13,009 13,010 13,011 13,012

less more

Properties

Parity: Even
Digit count: 5
Digit sum: 4
Digit product: 0
Digital root: 4
Palindrome: No
Bit width: 14 bits
Reversed: 31
Recamán's sequence: a(48,275) = 13,000
Square (n²): 169,000,000
Cube (n³): 2,197,000,000,000
Divisor count: 32
σ(n) — sum of divisors: 32,760
φ(n) — Euler's totient: 4,800
Sum of prime factors: 34

Primality

Prime factorization: 2 ³ × 5 ³ × 13

Nearest primes: 12,983 (−17) · 13,001 (+1)

Divisors & multiples

All divisors (32)

1 · 2 · 4 · 5 · 8 · 10 · 13 · 20 · 25 · 26 · 40 · 50 · 52 · 65 · 100 · 104 · 125 · 130 · 200 · 250 · 260 · 325 · 500 · 520 · 650 · 1000 · 1300 · 1625 · 2600 · 3250 · 6500 (half) · 13000

Aliquot sum (sum of proper divisors): 19,760

Factor pairs (a × b = 13,000)

1 × 13000

2 × 6500

4 × 3250

5 × 2600

8 × 1625

10 × 1300

13 × 1000

20 × 650

25 × 520

26 × 500

40 × 325

50 × 260

52 × 250

65 × 200

100 × 130

104 × 125

First multiples

13,000 · 26,000 (double) · 39,000 · 52,000 · 65,000 · 78,000 · 91,000 · 104,000 · 117,000 · 130,000

Sums & aliquot sequence

As a sum of two squares: 2² + 114² = 30² + 110² = 42² + 106² = 70² + 90²

As consecutive integers: 2,598 + 2,599 + 2,600 + 2,601 + 2,602 994 + 995 + … + 1,006 805 + 806 + … + 820 508 + 509 + … + 532

Aliquot sequence: 13,000 → 19,760 → 32,320 → 45,404 → 34,060 → 43,556 → 32,674 → 20,948 → 15,718 → 8,762 → 5,434 → 4,646 → 2,698 → 1,622 → 814 → 554 → 280 — unresolved within range

Continued fraction of √n

√13,000 = [114; (57, 228)]

Period length 2 — the block in parentheses repeats forever.

Representations

In words: thirteen thousand
Ordinal: 13000th
Binary: 11001011001000
Octal: 31310
Hexadecimal: 0x32C8
Base64: Msg=
One's complement: 52,535 (16-bit)
Scientific notation: 1.3 × 10⁴
As a duration: 13,000 s = 3 hours, 36 minutes, 40 seconds

In other bases

ternary (3) 122211111

quaternary (4) 3023020

quinary (5) 404000

senary (6) 140104

septenary (7) 52621

nonary (9) 18744

undecimal (11) 9849

duodecimal (12) 7634

tridecimal (13) 5bc0

tetradecimal (14) 4a48

pentadecimal (15) 3cba

As an angle

13,000° = 36 × 360° + 40°

40° ≈ 0.698 rad

Compass bearing: NE (northeast)

Why does a circle have 360 degrees? →

Historical numeral systems

Babylonian (base 60): 𒁹𒁹𒁹 𒌋𒌋𒌋𒁹𒁹𒁹𒁹𒁹𒁹 𒌋𒌋𒌋𒌋
Egyptian hieroglyphic: 𓂍𓆼𓆼𓆼
Greek (Milesian): ͵ιγ
Mayan (base 20): 𝋡·𝋬·𝋪·𝋠
Chinese: 一萬三千
Chinese (financial): 壹萬參仟

In other modern scripts

Eastern Arabic ١٣٠٠٠ Devanagari १३००० Bengali ১৩০০০ Tamil ௧௩௦௦௦ Thai ๑๓๐๐๐ Tibetan ༡༣༠༠༠ Khmer ១៣០០០ Lao ໑໓໐໐໐ Burmese ၁၃၀၀၀

Digit at this position in famous constants

π — Pi (π): Digit 13,000 = 9
e — Euler's number (e): Digit 13,000 = 2
φ — Golden ratio (φ): Digit 13,000 = 4
√2 — Pythagoras's (√2): Digit 13,000 = 1
ln 2 — Natural log of 2: Digit 13,000 = 6
γ — Euler-Mascheroni (γ): Digit 13,000 = 8

Also seen as

Goldbach decomposition

Goldbach's conjecture says every even integer greater than 2 is the sum of two primes. For 13000, here are decompositions:

17 + 12983 = 13000
41 + 12959 = 13000
47 + 12953 = 13000
59 + 12941 = 13000
83 + 12917 = 13000
89 + 12911 = 13000
101 + 12899 = 13000
107 + 12893 = 13000

Showing the first eight; more decompositions exist.

Unicode codepoint

㋈

Ideographic Telegraph Symbol For September

U+32C8

Other symbol (So)

UTF-8 encoding: E3 8B 88 (3 bytes).

Lookup U+32C8 on Compart ↗ Lookup on FileFormat.Info ↗

Hex color

#0032C8

RGB(0, 50, 200)

IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.0.50.200.

Address: 0.0.50.200
Class: reserved
IPv4-mapped IPv6: ::ffff:0.0.50.200

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

Musical pitch

Heard as a frequency, 13,000 Hz is closest to:

Concert pitch (A4 = 440 Hz): G♯9 (13289.8 Hz, -38¢)
Scientific pitch (C4 = 256 Hz): G♯9 (13004 Hz, -1¢)
Baroque pitch (A4 = 415 Hz): A9 (13280 Hz, -37¢)

Position in π

The digit sequence 13000 first appears in π at position 198,968 of the decimal expansion (the 198,968ordinal-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 13000 on Pi Search ↗