Live analysis

21,600

21,600 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.).

21,600 (twenty-one thousand six hundred) is an even 5-digit number. It is a composite number with 72 divisors, and factors as 2⁵ × 3³ × 5². Its proper divisors sum to 56,520, more than the number itself, making it an abundant number. Written other ways, in hexadecimal, 0x5460.

Abundant Number Achilles Number Arithmetic Number Gapful Number Harshad / Niven Odious Number Pernicious Number Powerful Number Practical Number Recamán's Sequence Refactorable Number Weird Number

Interestingness

★ ★ ★ ★ ★

9 notable facts · grade A

21,588 21,589 21,590 21,591 21,592 21,593 21,594 21,595 21,596 21,597 21,598 21,599 21,600 21,601 21,602 21,603 21,604 21,605 21,606 21,607 21,608 21,609 21,610 21,611 21,612

less more

Properties

Parity: Even
Digit count: 5
Digit sum: 9
Digit product: 0
Digital root: 9
Palindrome: No
Bit width: 15 bits
Reversed: 612
Recamán's sequence: a(40,639) = 21,600
Square (n²): 466,560,000
Cube (n³): 10,077,696,000,000
Divisor count: 72
σ(n) — sum of divisors: 78,120
φ(n) — Euler's totient: 5,760
Sum of prime factors: 29

Primality

Prime factorization: 2 ⁵ × 3 ³ × 5 ²

Nearest primes: 21,599 (−1) · 21,601 (+1)

Divisors & multiples

All divisors (72)

1 · 2 · 3 · 4 · 5 · 6 · 8 · 9 · 10 · 12 · 15 · 16 · 18 · 20 · 24 · 25 · 27 · 30 · 32 · 36 · 40 · 45 · 48 · 50 · 54 · 60 · 72 · 75 · 80 · 90 · 96 · 100 · 108 · 120 · 135 · 144 · 150 · 160 · 180 · 200 · 216 · 225 · 240 · 270 · 288 · 300 · 360 · 400 · 432 · 450 · 480 · 540 · 600 · 675 · 720 · 800 · 864 · 900 · 1080 · 1200 · 1350 · 1440 · 1800 · 2160 · 2400 · 2700 · 3600 · 4320 · 5400 · 7200 · 10800 (half) · 21600

Aliquot sum (sum of proper divisors): 56,520

Factor pairs (a × b = 21,600)

1 × 21600

2 × 10800

3 × 7200

4 × 5400

5 × 4320

6 × 3600

8 × 2700

9 × 2400

10 × 2160

12 × 1800

15 × 1440

16 × 1350

18 × 1200

20 × 1080

24 × 900

25 × 864

27 × 800

30 × 720

32 × 675

36 × 600

40 × 540

45 × 480

48 × 450

50 × 432

54 × 400

60 × 360

72 × 300

75 × 288

80 × 270

90 × 240

96 × 225

100 × 216

108 × 200

120 × 180

135 × 160

144 × 150

First multiples

21,600 · 43,200 (double) · 64,800 · 86,400 · 108,000 · 129,600 · 151,200 · 172,800 · 194,400 · 216,000

Sums & aliquot sequence

As consecutive integers: 7,199 + 7,200 + 7,201 4,318 + 4,319 + 4,320 + 4,321 + 4,322 2,396 + 2,397 + … + 2,404 1,433 + 1,434 + … + 1,447

Aliquot sequence: 21,600 → 56,520 → 128,340 → 290,988 → 462,492 → 749,628 → 1,373,892 → 2,078,844 → 2,802,564 → 4,281,786 → 4,995,456 → 8,274,744 → 15,521,256 → 26,515,674 → 33,063,846 → 33,137,562 → 33,137,574 — unresolved within range

Continued fraction of √n

√21,600 = [146; (1, 31, 1, 1, 1, 31, 1, 292)]

Period length 8 — the block in parentheses repeats forever.

Representations

In words: twenty-one thousand six hundred
Ordinal: 21600th
Binary: 101010001100000
Octal: 52140
Hexadecimal: 0x5460
Base64: VGA=
One's complement: 43,935 (16-bit)
Scientific notation: 2.16 × 10⁴
As a duration: 21,600 s = 6 hours

In other bases

ternary (3) 1002122000

quaternary (4) 11101200

quinary (5) 1142400

senary (6) 244000

septenary (7) 116655

nonary (9) 32560

undecimal (11) 15257

duodecimal (12) 10600

tridecimal (13) 9aa7

tetradecimal (14) 7c2c

pentadecimal (15) 6600

As an angle

21,600° = 60 × 360°

0° ≈ 0 rad

Compass bearing: N (north)

Why does a circle have 360 degrees? →

Historical numeral systems

Babylonian (base 60): 𒁹𒁹𒁹𒁹𒁹𒁹 · ·
Egyptian hieroglyphic: 𓂍𓂍𓆼𓍢𓍢𓍢𓍢𓍢𓍢
Greek (Milesian): ͵καχʹ
Mayan (base 20): 𝋢·𝋮·𝋠·𝋠
Chinese: 二萬一千六百
Chinese (financial): 貳萬壹仟陸佰

In other modern scripts

Eastern Arabic ٢١٦٠٠ Devanagari २१६०० Bengali ২১৬০০ Tamil ௨௧௬௦௦ Thai ๒๑๖๐๐ Tibetan ༢༡༦༠༠ Khmer ២១៦០០ Lao ໒໑໖໐໐ Burmese ၂၁၆၀၀

Digit at this position in famous constants

π — Pi (π): Digit 21,600 = 7
e — Euler's number (e): Digit 21,600 = 1
φ — Golden ratio (φ): Digit 21,600 = 2
√2 — Pythagoras's (√2): Digit 21,600 = 3
ln 2 — Natural log of 2: Digit 21,600 = 4
γ — Euler-Mascheroni (γ): Digit 21,600 = 3

Also seen as

Goldbach decomposition

Goldbach's conjecture says every even integer greater than 2 is the sum of two primes. For 21600, here are decompositions:

11 + 21589 = 21600
13 + 21587 = 21600
23 + 21577 = 21600
31 + 21569 = 21600
37 + 21563 = 21600
41 + 21559 = 21600
43 + 21557 = 21600
71 + 21529 = 21600

Showing the first eight; more decompositions exist.

Unicode codepoint

呠

CJK Unified Ideograph-5460

U+5460

Other letter (Lo)

UTF-8 encoding: E5 91 A0 (3 bytes).

Lookup U+5460 on Compart ↗ Lookup on FileFormat.Info ↗

Hex color

#005460

RGB(0, 84, 96)

IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.0.84.96.

Address: 0.0.84.96
Class: reserved
IPv4-mapped IPv6: ::ffff:0.0.84.96

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

Position in π

The digit sequence 21600 first appears in π at position 88,778 of the decimal expansion (the 88,778ordinal-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 21600 on Pi Search ↗