Live analysis

168,000

168,000 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.).

168,000 (one hundred sixty-eight thousand) is an even 6-digit number. It is a composite number with 112 divisors, and factors as 2⁶ × 3 × 5³ × 7. Its proper divisors sum to 465,984, more than the number itself, making it an abundant number. Written other ways, in hexadecimal, 0x29040.

Abundant Number Evil Number Flippable Gapful Number Harshad / Niven Practical Number Refactorable Number Weird Number

Interestingness

★ ★ ★ ★ ☆

6 notable facts · grade B

167,988 167,989 167,990 167,991 167,992 167,993 167,994 167,995 167,996 167,997 167,998 167,999 168,000 168,001 168,002 168,003 168,004 168,005 168,006 168,007 168,008 168,009 168,010 168,011 168,012

less more

Properties

Parity: Even
Digit count: 6
Digit sum: 15
Digit product: 0
Digital root: 6
Palindrome: No
Bit width: 18 bits
Reversed: 861
Flips to (rotate 180°): 891
Square (n²): 28,224,000,000
Cube (n³): 4,741,632,000,000,000
Divisor count: 112
σ(n) — sum of divisors: 633,984
φ(n) — Euler's totient: 38,400
Sum of prime factors: 37

Primality

Prime factorization: 2 ⁶ × 3 × 5 ³ × 7

Nearest primes: 167,987 (−13) · 168,013 (+13)

Divisors & multiples

All divisors (112)

1 · 2 · 3 · 4 · 5 · 6 · 7 · 8 · 10 · 12 · 14 · 15 · 16 · 20 · 21 · 24 · 25 · 28 · 30 · 32 · 35 · 40 · 42 · 48 · 50 · 56 · 60 · 64 · 70 · 75 · 80 · 84 · 96 · 100 · 105 · 112 · 120 · 125 · 140 · 150 · 160 · 168 · 175 · 192 · 200 · 210 · 224 · 240 · 250 · 280 · 300 · 320 · 336 · 350 · 375 · 400 · 420 · 448 · 480 · 500 · 525 · 560 · 600 · 672 · 700 · 750 · 800 · 840 · 875 · 960 · 1000 · 1050 · 1120 · 1200 · 1344 · 1400 · 1500 · 1600 · 1680 · 1750 · 2000 · 2100 · 2240 · 2400 · 2625 · 2800 · 3000 · 3360 · 3500 · 4000 · 4200 · 4800 · 5250 · 5600 · 6000 · 6720 · 7000 · 8000 · 8400 · 10500 · 11200 · 12000 · 14000 · 16800 · 21000 · 24000 · 28000 · 33600 · 42000 · 56000 · 84000 (half) · 168000

Aliquot sum (sum of proper divisors): 465,984

Factor pairs (a × b = 168,000)

1 × 168000

2 × 84000

3 × 56000

4 × 42000

5 × 33600

6 × 28000

7 × 24000

8 × 21000

10 × 16800

12 × 14000

14 × 12000

15 × 11200

16 × 10500

20 × 8400

21 × 8000

24 × 7000

25 × 6720

28 × 6000

30 × 5600

32 × 5250

35 × 4800

40 × 4200

42 × 4000

48 × 3500

50 × 3360

56 × 3000

60 × 2800

64 × 2625

70 × 2400

75 × 2240

80 × 2100

84 × 2000

96 × 1750

100 × 1680

105 × 1600

112 × 1500

120 × 1400

125 × 1344

140 × 1200

150 × 1120

160 × 1050

168 × 1000

175 × 960

192 × 875

200 × 840

210 × 800

224 × 750

240 × 700

250 × 672

280 × 600

300 × 560

320 × 525

336 × 500

350 × 480

375 × 448

400 × 420

First multiples

168,000 · 336,000 (double) · 504,000 · 672,000 · 840,000 · 1,008,000 · 1,176,000 · 1,344,000 · 1,512,000 · 1,680,000

Sums & aliquot sequence

As consecutive integers: 55,999 + 56,000 + 56,001 33,598 + 33,599 + 33,600 + 33,601 + 33,602 23,997 + 23,998 + … + 24,003 11,193 + 11,194 + … + 11,207

Aliquot sequence: 168,000 → 465,984 → 871,326 → 1,016,586 → 1,186,056 → 2,497,944 → 4,205,256 → 7,951,224 → 11,926,896 → 18,884,376 → 40,364,424 → 68,956,086 → 73,228,362 → 73,228,374 → 90,857,790 → 145,372,698 → 177,677,862 — unresolved within range

Continued fraction of √n

√168,000 = [409; (1, 7, 5, 32, 1, 1, 2, 7, 1, 3, 1, 31, 1, 203, 1, 31, 1, 3, 1, 7, 2, 1, 1, 32, …)]

Period length 28 — the block in parentheses repeats forever.

Representations

In words: one hundred sixty-eight thousand
Ordinal: 168000th
Binary: 101001000001000000
Octal: 510100
Hexadecimal: 0x29040
Base64: ApBA
One's complement: 4,294,799,295 (32-bit)
Scientific notation: 1.68 × 10⁵
As a duration: 168,000 s = 1 day, 22 hours, 40 minutes

In other bases

ternary (3) 22112110020

quaternary (4) 221001000

quinary (5) 20334000

senary (6) 3333440

septenary (7) 1266540

nonary (9) 275406

undecimal (11) 105248

duodecimal (12) 81280

tridecimal (13) 5b611

tetradecimal (14) 45320

pentadecimal (15) 34ba0

As an angle

168,000° = 466 × 360° + 240°

240° ≈ 4.189 rad

Compass bearing: WSW (west-southwest)

Why does a circle have 360 degrees? →

Historical numeral systems

Babylonian (base 60): 𒌋𒌋𒌋𒌋𒁹𒁹𒁹𒁹𒁹𒁹 𒌋𒌋𒌋𒌋 ·
Egyptian hieroglyphic: 𓆐𓂍𓂍𓂍𓂍𓂍𓂍𓆼𓆼𓆼𓆼𓆼𓆼𓆼𓆼
Greek (Milesian): ͵ρξη
Chinese: 一十六萬八千
Chinese (financial): 壹拾陸萬捌仟

In other modern scripts

Eastern Arabic ١٦٨٠٠٠ Devanagari १६८००० Bengali ১৬৮০০০ Tamil ௧௬௮௦௦௦ Thai ๑๖๘๐๐๐ Tibetan ༡༦༨༠༠༠ Khmer ១៦៨០០០ Lao ໑໖໘໐໐໐ Burmese ၁၆၈၀၀၀

Also seen as

Goldbach decomposition

Goldbach's conjecture says every even integer greater than 2 is the sum of two primes. For 168000, here are decompositions:

13 + 167987 = 168000
29 + 167971 = 168000
47 + 167953 = 168000
83 + 167917 = 168000
89 + 167911 = 168000
101 + 167899 = 168000
109 + 167891 = 168000
113 + 167887 = 168000

Showing the first eight; more decompositions exist.

Unicode codepoint

𩁀

CJK Unified Ideograph-29040

U+29040

Other letter (Lo)

UTF-8 encoding: F0 A9 81 80 (4 bytes).

Lookup U+29040 on Compart ↗ Lookup on FileFormat.Info ↗

Hex color

#029040

RGB(2, 144, 64)

IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.2.144.64.

Address: 0.2.144.64
Class: reserved
IPv4-mapped IPv6: ::ffff:0.2.144.64

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

Possible US patent number

This number falls in the range of US utility patent numbers. If it's a patent, it would be issued as US 168,000 and was likely granted around 1874.

Patent numbers below 100,000 are excluded as too ambiguous; modern numbering currently reaches roughly 12.5 million.

Look up US168,000 on Google Patents ↗ Look up on USPTO ↗

Position in π

The digit sequence 168000 first appears in π at position 461,628 of the decimal expansion (the 461,628ordinal-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 168000 on Pi Search ↗