Number

1,038

1,038 is a composite number, even, a calendar year.

1,038 (one thousand thirty-eight) is an even 4-digit number. It is a composite number with 8 divisors, and factors as 2 × 3 × 173. Its proper divisors sum to 1,050, more than the number itself, making it an abundant number. Written other ways, in Roman numerals it is MXXXVIII and in binary, 10000001110.

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

Interestingness

★ ★ ★ ★ ☆

6 notable facts · grade B

1,026 1,027 1,028 1,029 1,030 1,031 1,032 1,033 1,034 1,035 1,036 1,037 1,038 1,039 1,040 1,041 1,042 1,043 1,044 1,045 1,046 1,047 1,048 1,049 1,050

less more

Historical context — 1038 AD

Calendar year

Year 1038 (MXXXVIII) was a common year starting on Sunday of the Julian calendar.

Excerpt from Wikipedia (en) ↗ · Licensed CC BY-SA 4.0 Read the full article on Wikipedia →

Year facts

Year type: Common year
Standard 365-day year; not divisible by 4 (or divisible by 100 but not 400).
Days in year: 365
ISO weeks: 52
Started on: Monday
January 1, 1038
Ended on: Monday
December 31, 1038
Friday the 13ths: 2
2 Friday the 13ths this year.
Decade: 1030s
1030–1039
Century: 11th century
1001–1100
Millennium: 2nd millennium
1001–2000
Years ago: 988
988 years before 2026.

In other calendars

Hebrew: 4798 / 4799 AM
Rosh Hashanah falls in September/October.
Islamic Hijri: 429 / 430 AH
Lunar calendar; year spans differ from Gregorian.
Chinese: Year of the zodiac:Earth zodiac:Tiger
Sexagenary cycle position 15 of 60. Lunar new year falls in late January / mid-February.
Buddhist Era: 1581 BE
Counted from the parinirvana of the Buddha (Theravada / Thai / Sri Lankan convention).
Persian Solar Hijri: 416 / 417 SH
Iranian calendar; Nowruz (new year) falls on the spring equinox.
Ethiopian: 1030 / 1031 ET
Year boundary at Enkutatash (September 11/12).
Indian National (Saka): 960 / 959 Saka
Indian national calendar; year starts in March.

Properties

Parity: Even
Digit count: 4
Digit sum: 12
Digit product: 0
Digital root: 3
Palindrome: No
Bit width: 11 bits
Reversed: 8,301
Recamán's sequence: a(4,343) = 1,038
Square (n²): 1,077,444
Cube (n³): 1,118,386,872
Divisor count: 8
σ(n) — sum of divisors: 2,088
φ(n) — Euler's totient: 344
Sum of prime factors: 178

Primality

Prime factorization: 2 × 3 × 173

Nearest primes: 1,033 (−5) · 1,039 (+1)

Divisors & multiples

All divisors (8)

1 · 2 · 3 · 6 · 173 · 346 · 519 (half) · 1038

Aliquot sum (sum of proper divisors): 1,050

Factor pairs (a × b = 1,038)

1 × 1038

2 × 519

3 × 346

6 × 173

First multiples

1,038 · 2,076 (double) · 3,114 · 4,152 · 5,190 · 6,228 · 7,266 · 8,304 · 9,342 · 10,380

Sums & aliquot sequence

As consecutive integers: 345 + 346 + 347 258 + 259 + 260 + 261 81 + 82 + … + 92

Aliquot sequence: 1,038 → 1,050 → 1,926 → 2,286 → 2,706 → 3,342 → 3,354 → 4,038 → 4,050 → 7,203 → 4,001 → 1 → 0 — terminates at zero

Continued fraction of √n

√1,038 = [32; (4, 1, 1, 2, 2, 1, 2, 10, 2, 1, 2, 2, 1, 1, 4, 64)]

Period length 16 — the block in parentheses repeats forever.

Representations

In words: one thousand thirty-eight
Ordinal: 1038th
Roman numeral: MXXXVIII
Binary: 10000001110
Octal: 2016
Hexadecimal: 0x40E
Base64: BA4=
One's complement: 64,497 (16-bit)
Scientific notation: 1.038 × 10³
As a duration: 1,038 s = 17 minutes, 18 seconds

In other bases

ternary (3) 1102110

quaternary (4) 100032

quinary (5) 13123

senary (6) 4450

septenary (7) 3012

nonary (9) 1373

undecimal (11) 864

duodecimal (12) 726

tridecimal (13) 61b

tetradecimal (14) 542

pentadecimal (15) 493

As an angle

1,038° = 2 × 360° + 318°

318° ≈ 5.55 rad

Compass bearing: NW (northwest)

Why does a circle have 360 degrees? →

Historical numeral systems

Babylonian (base 60): 𒌋𒁹𒁹𒁹𒁹𒁹𒁹𒁹 𒌋𒁹𒁹𒁹𒁹𒁹𒁹𒁹𒁹
Egyptian hieroglyphic: 𓆼𓎆𓎆𓎆𓏺𓏺𓏺𓏺𓏺𓏺𓏺𓏺
Greek (Milesian): ͵αληʹ
Mayan (base 20): 𝋢·𝋫·𝋲
Chinese: 一千零三十八
Chinese (financial): 壹仟零參拾捌

In other modern scripts

Eastern Arabic ١٠٣٨ Devanagari १०३८ Bengali ১০৩৮ Tamil ௧௦௩௮ Thai ๑๐๓๘ Tibetan ༡༠༣༨ Khmer ១០៣៨ Lao ໑໐໓໘ Burmese ၁၀၃၈

Digit at this position in famous constants

π — Pi (π): Digit 1,038 = 2
e — Euler's number (e): Digit 1,038 = 8
φ — Golden ratio (φ): Digit 1,038 = 1
√2 — Pythagoras's (√2): Digit 1,038 = 2
ln 2 — Natural log of 2: Digit 1,038 = 9
γ — Euler-Mascheroni (γ): Digit 1,038 = 7

Also seen as

Goldbach decomposition

Goldbach's conjecture says every even integer greater than 2 is the sum of two primes. For 1038, here are decompositions:

5 + 1033 = 1038
7 + 1031 = 1038
17 + 1021 = 1038
19 + 1019 = 1038
29 + 1009 = 1038
41 + 997 = 1038
47 + 991 = 1038
61 + 977 = 1038

Showing the first eight; more decompositions exist.

Unicode codepoint

Cyrillic Capital Letter Short U

U+040E

Uppercase letter (Lu)

UTF-8 encoding: D0 8E (2 bytes).

Lookup U+040E on Compart ↗ Lookup on FileFormat.Info ↗

Hex color

#00040E

RGB(0, 4, 14)

IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.0.4.14.

Address: 0.0.4.14
Class: reserved
IPv4-mapped IPv6: ::ffff:0.0.4.14

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

Musical pitch

Heard as a frequency, 1,038 Hz is closest to:

Concert pitch (A4 = 440 Hz): C6 (1046.5 Hz, -14¢)
Scientific pitch (C4 = 256 Hz): C6 (1024 Hz, +24¢)
Baroque pitch (A4 = 415 Hz): C♯6 (1045.7 Hz, -13¢)

Position in π

The digit sequence 1038 first appears in π at position 5,326 of the decimal expansion (the 5,326ordinal-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 1038 on Pi Search ↗