Live analysis

107,988

107,988 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.).

107,988 (one hundred seven thousand nine hundred eighty-eight) is an even 6-digit number. It is a composite number with 12 divisors, and factors as 2² × 3 × 8,999. Its proper divisors sum to 144,012, more than the number itself, making it an abundant number. Written other ways, in hexadecimal, 0x1A5D4.

Abundant Number Arithmetic Number Cube-Free Odious Number Recamán's Sequence Refactorable Number Semiperfect Number

Interestingness

★ ★ ★ ☆ ☆

5 notable facts · grade C

107,976 107,977 107,978 107,979 107,980 107,981 107,982 107,983 107,984 107,985 107,986 107,987 107,988 107,989 107,990 107,991 107,992 107,993 107,994 107,995 107,996 107,997 107,998 107,999 108,000

less more

Properties

Parity: Even
Digit count: 6
Digit sum: 33
Digit product: 0
Digital root: 6
Palindrome: No
Bit width: 17 bits
Reversed: 889,701
Recamán's sequence: a(46,715) = 107,988
Square (n²): 11,661,408,144
Cube (n³): 1,259,292,142,654,272
Divisor count: 12
σ(n) — sum of divisors: 252,000
φ(n) — Euler's totient: 35,992
Sum of prime factors: 9,006

Primality

Prime factorization: 2 ² × 3 × 8999

Nearest primes: 107,981 (−7) · 107,999 (+11)

Divisors & multiples

All divisors (12)

1 · 2 · 3 · 4 · 6 · 12 · 8999 · 17998 · 26997 · 35996 · 53994 (half) · 107988

Aliquot sum (sum of proper divisors): 144,012

Factor pairs (a × b = 107,988)

1 × 107988

2 × 53994

3 × 35996

4 × 26997

6 × 17998

12 × 8999

First multiples

107,988 · 215,976 (double) · 323,964 · 431,952 · 539,940 · 647,928 · 755,916 · 863,904 · 971,892 · 1,079,880

Sums & aliquot sequence

As consecutive integers: 35,995 + 35,996 + 35,997 13,495 + 13,496 + … + 13,502 4,488 + 4,489 + … + 4,511

Aliquot sequence: 107,988 → 144,012 → 222,900 → 422,892 → 710,604 → 1,085,736 → 1,772,664 → 2,692,056 → 4,081,704 → 7,050,936 → 10,779,864 → 16,169,856 → 29,326,224 → 52,043,568 → 84,304,848 → 134,320,048 → 130,193,280 — unresolved within range

Continued fraction of √n

√107,988 = [328; (1, 1, 1, 1, 2, 54, 2, 1, 1, 1, 1, 656)]

Period length 12 — the block in parentheses repeats forever.

Representations

In words: one hundred seven thousand nine hundred eighty-eight
Ordinal: 107988th
Binary: 11010010111010100
Octal: 322724
Hexadecimal: 0x1A5D4
Base64: AaXU
One's complement: 4,294,859,307 (32-bit)
Scientific notation: 1.07988 × 10⁵
As a duration: 107,988 s = 1 day, 5 hours, 59 minutes, 48 seconds

In other bases

ternary (3) 12111010120

quaternary (4) 122113110

quinary (5) 11423423

senary (6) 2151540

septenary (7) 626556

nonary (9) 174116

undecimal (11) 74151

duodecimal (12) 525b0

tridecimal (13) 3a1ca

tetradecimal (14) 2b4d6

pentadecimal (15) 21ee3

As an angle

107,988° = 299 × 360° + 348°

348° ≈ 6.074 rad

Compass bearing: NNW (north-northwest)

Why does a circle have 360 degrees? →

Historical numeral systems

Babylonian (base 60): 𒌋𒌋𒁹𒁹𒁹𒁹𒁹𒁹𒁹𒁹𒁹 𒌋𒌋𒌋𒌋𒌋𒁹𒁹𒁹𒁹𒁹𒁹𒁹𒁹𒁹 𒌋𒌋𒌋𒌋𒁹𒁹𒁹𒁹𒁹𒁹𒁹𒁹
Egyptian hieroglyphic: 𓆐𓆼𓆼𓆼𓆼𓆼𓆼𓆼𓍢𓍢𓍢𓍢𓍢𓍢𓍢𓍢𓍢𓎆𓎆𓎆𓎆𓎆𓎆𓎆𓎆𓏺𓏺𓏺𓏺𓏺𓏺𓏺𓏺
Greek (Milesian): ͵ρζϡπηʹ
Mayan (base 20): 𝋭·𝋩·𝋳·𝋨
Chinese: 十萬七千九百八十八
Chinese (financial): 壹拾萬柒仟玖佰捌拾捌

In other modern scripts

Eastern Arabic ١٠٧٩٨٨ Devanagari १०७९८८ Bengali ১০৭৯৮৮ Tamil ௧௦௭௯௮௮ Thai ๑๐๗๙๘๘ Tibetan ༡༠༧༩༨༨ Khmer ១០៧៩៨៨ Lao ໑໐໗໙໘໘ Burmese ၁၀၇၉၈၈

Also seen as

Goldbach decomposition

Goldbach's conjecture says every even integer greater than 2 is the sum of two primes. For 107988, here are decompositions:

7 + 107981 = 107988
17 + 107971 = 107988
37 + 107951 = 107988
47 + 107941 = 107988
61 + 107927 = 107988
107 + 107881 = 107988
131 + 107857 = 107988
149 + 107839 = 107988

Showing the first eight; more decompositions exist.

Hex color

#01A5D4

RGB(1, 165, 212)

IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.1.165.212.

Address: 0.1.165.212
Class: reserved
IPv4-mapped IPv6: ::ffff:0.1.165.212

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 107,988 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 US107,988 on Google Patents ↗ Look up on USPTO ↗

Position in π

The digit sequence 107988 first appears in π at position 708,079 of the decimal expansion (the 708,079ordinal-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 107988 on Pi Search ↗