Live analysis

10,038

10,038 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.).

10,038 (ten thousand thirty-eight) is an even 5-digit number. It is a composite number with 16 divisors, and factors as 2 × 3 × 7 × 239. Its proper divisors sum to 13,002, more than the number itself, making it an abundant number. Written other ways, in hexadecimal, 0x2736.

Abundant Number Arithmetic Number Cube-Free Evil Number Recamán's Sequence Semiperfect Number Squarefree

Interestingness

★ ★ ★ ☆ ☆

5 notable facts · grade C

10,026 10,027 10,028 10,029 10,030 10,031 10,032 10,033 10,034 10,035 10,036 10,037 10,038 10,039 10,040 10,041 10,042 10,043 10,044 10,045 10,046 10,047 10,048 10,049 10,050

less more

Properties

Parity: Even
Digit count: 5
Digit sum: 12
Digit product: 0
Digital root: 3
Palindrome: No
Bit width: 14 bits
Reversed: 83,001
Recamán's sequence: a(4,863) = 10,038
Square (n²): 100,761,444
Cube (n³): 1,011,443,374,872
Divisor count: 16
σ(n) — sum of divisors: 23,040
φ(n) — Euler's totient: 2,856
Sum of prime factors: 251

Primality

Prime factorization: 2 × 3 × 7 × 239

Nearest primes: 10,037 (−1) · 10,039 (+1)

Divisors & multiples

All divisors (16)

1 · 2 · 3 · 6 · 7 · 14 · 21 · 42 · 239 · 478 · 717 · 1434 · 1673 · 3346 · 5019 (half) · 10038

Aliquot sum (sum of proper divisors): 13,002

Factor pairs (a × b = 10,038)

1 × 10038

2 × 5019

3 × 3346

6 × 1673

7 × 1434

14 × 717

21 × 478

42 × 239

First multiples

10,038 · 20,076 (double) · 30,114 · 40,152 · 50,190 · 60,228 · 70,266 · 80,304 · 90,342 · 100,380

Sums & aliquot sequence

As consecutive integers: 3,345 + 3,346 + 3,347 2,508 + 2,509 + 2,510 + 2,511 1,431 + 1,432 + … + 1,437 831 + 832 + … + 842

Aliquot sequence: 10,038 → 13,002 → 15,510 → 25,962 → 25,974 → 37,866 → 37,878 → 39,882 → 48,534 → 48,546 → 66,654 → 105,882 → 136,230 → 209,370 → 365,478 → 365,490 → 622,926 — unresolved within range

Continued fraction of √n

√10,038 = [100; (5, 3, 1, 2, 1, 2, 3, 1, 8, 1, 3, 2, 1, 2, 1, 3, 5, 200)]

Period length 18 — the block in parentheses repeats forever.

Representations

In words: ten thousand thirty-eight
Ordinal: 10038th
Binary: 10011100110110
Octal: 23466
Hexadecimal: 0x2736
Base64: JzY=
One's complement: 55,497 (16-bit)
Scientific notation: 1.0038 × 10⁴
As a duration: 10,038 s = 2 hours, 47 minutes, 18 seconds

In other bases

ternary (3) 111202210

quaternary (4) 2130312

quinary (5) 310123

senary (6) 114250

septenary (7) 41160

nonary (9) 14683

undecimal (11) 75a6

duodecimal (12) 5986

tridecimal (13) 4752

tetradecimal (14) 3930

pentadecimal (15) 2e93

Palindromic in base 4

As an angle

10,038° = 27 × 360° + 318°

318° ≈ 5.55 rad

Compass bearing: NW (northwest)

Why does a circle have 360 degrees? →

Historical numeral systems

Babylonian (base 60): 𒁹𒁹 𒌋𒌋𒌋𒌋𒁹𒁹𒁹𒁹𒁹𒁹𒁹 𒌋𒁹𒁹𒁹𒁹𒁹𒁹𒁹𒁹
Egyptian hieroglyphic: 𓂍𓎆𓎆𓎆𓏺𓏺𓏺𓏺𓏺𓏺𓏺𓏺
Greek (Milesian): ͵ιληʹ
Mayan (base 20): 𝋡·𝋥·𝋡·𝋲
Chinese: 一萬零三十八
Chinese (financial): 壹萬零參拾捌

In other modern scripts

Eastern Arabic ١٠٠٣٨ Devanagari १००३८ Bengali ১০০৩৮ Tamil ௧௦௦௩௮ Thai ๑๐๐๓๘ Tibetan ༡༠༠༣༨ Khmer ១០០៣៨ Lao ໑໐໐໓໘ Burmese ၁၀၀၃၈

Digit at this position in famous constants

π — Pi (π): Digit 10,038 = 7
e — Euler's number (e): Digit 10,038 = 0
φ — Golden ratio (φ): Digit 10,038 = 7
√2 — Pythagoras's (√2): Digit 10,038 = 8
ln 2 — Natural log of 2: Digit 10,038 = 0
γ — Euler-Mascheroni (γ): Digit 10,038 = 1

Also seen as

Goldbach decomposition

Goldbach's conjecture says every even integer greater than 2 is the sum of two primes. For 10038, here are decompositions:

29 + 10009 = 10038
31 + 10007 = 10038
71 + 9967 = 10038
89 + 9949 = 10038
97 + 9941 = 10038
107 + 9931 = 10038
109 + 9929 = 10038
131 + 9907 = 10038

Showing the first eight; more decompositions exist.

Unicode codepoint

✶

Six Pointed Black Star

U+2736

Other symbol (So)

UTF-8 encoding: E2 9C B6 (3 bytes).

Lookup U+2736 on Compart ↗ Lookup on FileFormat.Info ↗

Hex color

#002736

RGB(0, 39, 54)

IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.0.39.54.

Address: 0.0.39.54
Class: reserved
IPv4-mapped IPv6: ::ffff:0.0.39.54

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

Musical pitch

Heard as a frequency, 10,038 Hz is closest to:

Concert pitch (A4 = 440 Hz): D♯9 (9956.1 Hz, +14¢)
Scientific pitch (C4 = 256 Hz): E9 (10321.3 Hz, -48¢ — about midway to D♯9)
Baroque pitch (A4 = 415 Hz): E9 (9948.8 Hz, +15¢)

Position in π

The digit sequence 10038 first appears in π at position 71,744 of the decimal expansion (the 71,744ordinal-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 10038 on Pi Search ↗