Live analysis

105,984

105,984 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.).

105,984 (one hundred five thousand nine hundred eighty-four) is an even 6-digit number. It is a composite number with 60 divisors, and factors as 2⁹ × 3² × 23. Its proper divisors sum to 213,192, more than the number itself, making it an abundant number. Written other ways, in hexadecimal, 0x19E00.

Abundant Number Evil Number Practical Number Recamán's Sequence Semiperfect Number

Interestingness

★ ☆ ☆ ☆ ☆

3 notable facts · grade F

105,972 105,973 105,974 105,975 105,976 105,977 105,978 105,979 105,980 105,981 105,982 105,983 105,984 105,985 105,986 105,987 105,988 105,989 105,990 105,991 105,992 105,993 105,994 105,995 105,996

less more

Properties

Parity: Even
Digit count: 6
Digit sum: 27
Digit product: 0
Digital root: 9
Palindrome: No
Bit width: 17 bits
Reversed: 489,501
Recamán's sequence: a(89,203) = 105,984
Square (n²): 11,232,608,256
Cube (n³): 1,190,476,753,403,904
Divisor count: 60
σ(n) — sum of divisors: 319,176
φ(n) — Euler's totient: 33,792
Sum of prime factors: 47

Primality

Prime factorization: 2 ⁹ × 3 ² × 23

Nearest primes: 105,983 (−1) · 105,997 (+13)

Divisors & multiples

All divisors (60)

1 · 2 · 3 · 4 · 6 · 8 · 9 · 12 · 16 · 18 · 23 · 24 · 32 · 36 · 46 · 48 · 64 · 69 · 72 · 92 · 96 · 128 · 138 · 144 · 184 · 192 · 207 · 256 · 276 · 288 · 368 · 384 · 414 · 512 · 552 · 576 · 736 · 768 · 828 · 1104 · 1152 · 1472 · 1536 · 1656 · 2208 · 2304 · 2944 · 3312 · 4416 · 4608 · 5888 · 6624 · 8832 · 11776 · 13248 · 17664 · 26496 · 35328 · 52992 (half) · 105984

Aliquot sum (sum of proper divisors): 213,192

Factor pairs (a × b = 105,984)

1 × 105984

2 × 52992

3 × 35328

4 × 26496

6 × 17664

8 × 13248

9 × 11776

12 × 8832

16 × 6624

18 × 5888

23 × 4608

24 × 4416

32 × 3312

36 × 2944

46 × 2304

48 × 2208

64 × 1656

69 × 1536

72 × 1472

92 × 1152

96 × 1104

128 × 828

138 × 768

144 × 736

184 × 576

192 × 552

207 × 512

256 × 414

276 × 384

288 × 368

First multiples

105,984 · 211,968 (double) · 317,952 · 423,936 · 529,920 · 635,904 · 741,888 · 847,872 · 953,856 · 1,059,840

Sums & aliquot sequence

As consecutive integers: 35,327 + 35,328 + 35,329 11,772 + 11,773 + … + 11,780 4,597 + 4,598 + … + 4,619 1,502 + 1,503 + … + 1,570

Aliquot sequence: 105,984 → 213,192 → 483,768 → 826,632 → 1,549,368 → 2,807,712 → 5,177,538 → 6,631,662 → 7,089,378 → 7,089,390 → 17,425,170 → 37,431,918 → 46,308,258 → 54,026,340 → 106,148,892 → 142,648,804 → 106,986,610 — unresolved within range

Continued fraction of √n

√105,984 = [325; (1, 1, 4, 3, 10, 40, 1, 1, 2, 12, 1, 7, 1, 161, 1, 7, 1, 12, 2, 1, 1, 40, 10, 3, …)]

Period length 28 — the block in parentheses repeats forever.

Representations

In words: one hundred five thousand nine hundred eighty-four
Ordinal: 105984th
Binary: 11001111000000000
Octal: 317000
Hexadecimal: 0x19E00
Base64: AZ4A
One's complement: 4,294,861,311 (32-bit)
Scientific notation: 1.05984 × 10⁵
As a duration: 105,984 s = 1 day, 5 hours, 26 minutes, 24 seconds

In other bases

ternary (3) 12101101100

quaternary (4) 121320000

quinary (5) 11342414

senary (6) 2134400

septenary (7) 620664

nonary (9) 171340

undecimal (11) 7269a

duodecimal (12) 51400

tridecimal (13) 39318

tetradecimal (14) 2a8a4

pentadecimal (15) 21609

As an angle

105,984° = 294 × 360° + 144°

144° ≈ 2.513 rad

Compass bearing: SE (southeast)

Why does a circle have 360 degrees? →

Historical numeral systems

Babylonian (base 60): 𒌋𒌋𒁹𒁹𒁹𒁹𒁹𒁹𒁹𒁹𒁹 𒌋𒌋𒁹𒁹𒁹𒁹𒁹𒁹 𒌋𒌋𒁹𒁹𒁹𒁹
Egyptian hieroglyphic: 𓆐𓆼𓆼𓆼𓆼𓆼𓍢𓍢𓍢𓍢𓍢𓍢𓍢𓍢𓍢𓎆𓎆𓎆𓎆𓎆𓎆𓎆𓎆𓏺𓏺𓏺𓏺
Greek (Milesian): ͵ρεϡπδʹ
Mayan (base 20): 𝋭·𝋤·𝋳·𝋤
Chinese: 一十萬五千九百八十四
Chinese (financial): 壹拾萬伍仟玖佰捌拾肆

In other modern scripts

Eastern Arabic ١٠٥٩٨٤ Devanagari १०५९८४ Bengali ১০৫৯৮৪ Tamil ௧௦௫௯௮௪ Thai ๑๐๕๙๘๔ Tibetan ༡༠༥༩༨༤ Khmer ១០៥៩៨៤ Lao ໑໐໕໙໘໔ Burmese ၁၀၅၉၈၄

Also seen as

Goldbach decomposition

Goldbach's conjecture says every even integer greater than 2 is the sum of two primes. For 105984, here are decompositions:

7 + 105977 = 105984
13 + 105971 = 105984
17 + 105967 = 105984
31 + 105953 = 105984
41 + 105943 = 105984
71 + 105913 = 105984
101 + 105883 = 105984
113 + 105871 = 105984

Showing the first eight; more decompositions exist.

Hex color

#019E00

RGB(1, 158, 0)

IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.1.158.0.

Address: 0.1.158.0
Class: reserved
IPv4-mapped IPv6: ::ffff:0.1.158.0

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 105,984 and was likely granted around 1870.

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

Look up US105,984 on Google Patents ↗ Look up on USPTO ↗

Position in π

The digit sequence 105984 first appears in π at position 483,464 of the decimal expansion (the 483,464ordinal-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 105984 on Pi Search ↗