Live analysis

13,500

13,500 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.).

13,500 (thirteen thousand five hundred) is an even 5-digit number. It is a composite number with 48 divisors, and factors as 2² × 3³ × 5³. Its proper divisors sum to 30,180, more than the number itself, making it an abundant number. Written other ways, in hexadecimal, 0x34BC.

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

Interestingness

★ ★ ★ ★ ★

8 notable facts · grade A

13,488 13,489 13,490 13,491 13,492 13,493 13,494 13,495 13,496 13,497 13,498 13,499 13,500 13,501 13,502 13,503 13,504 13,505 13,506 13,507 13,508 13,509 13,510 13,511 13,512

less more

Properties

Parity: Even
Digit count: 5
Digit sum: 9
Digit product: 0
Digital root: 9
Palindrome: No
Bit width: 14 bits
Reversed: 531
Recamán's sequence: a(47,275) = 13,500
Square (n²): 182,250,000
Cube (n³): 2,460,375,000,000
Divisor count: 48
σ(n) — sum of divisors: 43,680
φ(n) — Euler's totient: 3,600
Sum of prime factors: 28

Primality

Prime factorization: 2 ² × 3 ³ × 5 ³

Nearest primes: 13,499 (−1) · 13,513 (+13)

Divisors & multiples

All divisors (48)

1 · 2 · 3 · 4 · 5 · 6 · 9 · 10 · 12 · 15 · 18 · 20 · 25 · 27 · 30 · 36 · 45 · 50 · 54 · 60 · 75 · 90 · 100 · 108 · 125 · 135 · 150 · 180 · 225 · 250 · 270 · 300 · 375 · 450 · 500 · 540 · 675 · 750 · 900 · 1125 · 1350 · 1500 · 2250 · 2700 · 3375 · 4500 · 6750 (half) · 13500

Aliquot sum (sum of proper divisors): 30,180

Factor pairs (a × b = 13,500)

1 × 13500

2 × 6750

3 × 4500

4 × 3375

5 × 2700

6 × 2250

9 × 1500

10 × 1350

12 × 1125

15 × 900

18 × 750

20 × 675

25 × 540

27 × 500

30 × 450

36 × 375

45 × 300

50 × 270

54 × 250

60 × 225

75 × 180

90 × 150

100 × 135

108 × 125

First multiples

13,500 · 27,000 (double) · 40,500 · 54,000 · 67,500 · 81,000 · 94,500 · 108,000 · 121,500 · 135,000

Sums & aliquot sequence

As consecutive integers: 4,499 + 4,500 + 4,501 2,698 + 2,699 + 2,700 + 2,701 + 2,702 1,684 + 1,685 + … + 1,691 1,496 + 1,497 + … + 1,504

Aliquot sequence: 13,500 → 30,180 → 54,492 → 79,908 → 106,572 → 147,444 → 228,204 → 363,716 → 281,404 → 211,060 → 242,036 → 181,534 → 93,146 → 46,576 → 47,168 → 56,464 → 52,966 — unresolved within range

Continued fraction of √n

√13,500 = [116; (5, 3, 1, 1, 1, 1, 3, 1, 1, 5, 1, 8, 2, 4, 3, 1, 2, 1, 1, 25, 4, 9, 21, 58, …)]

Period length 48 — the block in parentheses repeats forever.

Representations

In words: thirteen thousand five hundred
Ordinal: 13500th
Binary: 11010010111100
Octal: 32274
Hexadecimal: 0x34BC
Base64: NLw=
One's complement: 52,035 (16-bit)
Scientific notation: 1.35 × 10⁴
As a duration: 13,500 s = 3 hours, 45 minutes

In other bases

ternary (3) 200112000

quaternary (4) 3102330

quinary (5) 413000

senary (6) 142300

septenary (7) 54234

nonary (9) 20460

undecimal (11) a163

duodecimal (12) 7990

tridecimal (13) 61b6

tetradecimal (14) 4cc4

pentadecimal (15) 4000

Palindromic in base 14

As an angle

13,500° = 37 × 360° + 180°

180° ≈ 3.142 rad

Compass bearing: S (south)

Why does a circle have 360 degrees? →

Historical numeral systems

Babylonian (base 60): 𒁹𒁹𒁹 𒌋𒌋𒌋𒌋𒁹𒁹𒁹𒁹𒁹 ·
Egyptian hieroglyphic: 𓂍𓆼𓆼𓆼𓍢𓍢𓍢𓍢𓍢
Greek (Milesian): ͵ιγφʹ
Mayan (base 20): 𝋡·𝋭·𝋯·𝋠
Chinese: 一萬三千五百
Chinese (financial): 壹萬參仟伍佰

In other modern scripts

Eastern Arabic ١٣٥٠٠ Devanagari १३५०० Bengali ১৩৫০০ Tamil ௧௩௫௦௦ Thai ๑๓๕๐๐ Tibetan ༡༣༥༠༠ Khmer ១៣៥០០ Lao ໑໓໕໐໐ Burmese ၁၃၅၀၀

Digit at this position in famous constants

π — Pi (π): Digit 13,500 = 8
e — Euler's number (e): Digit 13,500 = 1
φ — Golden ratio (φ): Digit 13,500 = 7
√2 — Pythagoras's (√2): Digit 13,500 = 0
ln 2 — Natural log of 2: Digit 13,500 = 5
γ — Euler-Mascheroni (γ): Digit 13,500 = 9

Also seen as

Goldbach decomposition

Goldbach's conjecture says every even integer greater than 2 is the sum of two primes. For 13500, here are decompositions:

13 + 13487 = 13500
23 + 13477 = 13500
31 + 13469 = 13500
37 + 13463 = 13500
43 + 13457 = 13500
59 + 13441 = 13500
79 + 13421 = 13500
83 + 13417 = 13500

Showing the first eight; more decompositions exist.

Unicode codepoint

㒼

CJK Unified Ideograph-34Bc

U+34BC

Other letter (Lo)

UTF-8 encoding: E3 92 BC (3 bytes).

Lookup U+34BC on Compart ↗ Lookup on FileFormat.Info ↗

Hex color

#0034BC

RGB(0, 52, 188)

IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.0.52.188.

Address: 0.0.52.188
Class: reserved
IPv4-mapped IPv6: ::ffff:0.0.52.188

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

Musical pitch

Heard as a frequency, 13,500 Hz is closest to:

Concert pitch (A4 = 440 Hz): G♯9 (13289.8 Hz, +27¢)
Scientific pitch (C4 = 256 Hz): A9 (13777.2 Hz, -35¢)
Baroque pitch (A4 = 415 Hz): A9 (13280 Hz, +28¢)

Position in π

The digit sequence 13500 first appears in π at position 21,027 of the decimal expansion (the 21,027ordinal-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 13500 on Pi Search ↗