Number

1,638

1,638 is a composite number, even, a calendar year.

1,638 (one thousand six hundred thirty-eight) is an even 4-digit number. It is a composite number with 24 divisors, and factors as 2 × 3² × 7 × 13. Its proper divisors sum to 2,730, more than the number itself, making it an abundant number. Written other ways, in Roman numerals it is MDCXXXVIII and in binary, 11001100110.

Abundant Number Arithmetic Number Cube-Free Evil Number Gapful Number Harshad / Niven Practical Number Recamán's Sequence Self Number Semiperfect Number Year

Interestingness

★ ★ ★ ★ ★

8 notable facts · grade A

1,626 1,627 1,628 1,629 1,630 1,631 1,632 1,633 1,634 1,635 1,636 1,637 1,638 1,639 1,640 1,641 1,642 1,643 1,644 1,645 1,646 1,647 1,648 1,649 1,650

less more

Notable events — 1638 AD

Feb 28 Scotland's National Covenant is signed against Charles I's religious policies.
Apr 15 The Shimabara Rebellion is crushed in Japan.
May 12 Dutch settlers establish New Sweden on the Delaware.

Events compiled from Wikipedia ↗ · Licensed CC BY-SA 4.0

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: Friday
January 1, 1638
Ended on: Friday
December 31, 1638
Friday the 13ths: 1
One Friday the 13th this year.
Easter Sunday: April 4
Sunday, April 4, 1638
Decade: 1630s
1630–1639
Century: 17th century
1601–1700
Millennium: 2nd millennium
1001–2000
Years ago: 388
388 years before 2026.

In other calendars

Hebrew: 5398 / 5399 AM
Rosh Hashanah falls in September/October.
Islamic Hijri: 1047 / 1048 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: 2181 BE
Counted from the parinirvana of the Buddha (Theravada / Thai / Sri Lankan convention).
Persian Solar Hijri: 1016 / 1017 SH
Iranian calendar; Nowruz (new year) falls on the spring equinox.
Ethiopian: 1630 / 1631 ET
Year boundary at Enkutatash (September 11/12).
Indian National (Saka): 1560 / 1559 Saka
Indian national calendar; year starts in March.

Properties

Parity: Even
Digit count: 4
Digit sum: 18
Digit product: 144
Digital root: 9
Palindrome: No
Bit width: 11 bits
Reversed: 8,361
Recamán's sequence: a(676) = 1,638
Square (n²): 2,683,044
Cube (n³): 4,394,826,072
Divisor count: 24
σ(n) — sum of divisors: 4,368
φ(n) — Euler's totient: 432
Sum of prime factors: 28

Primality

Prime factorization: 2 × 3 ² × 7 × 13

Nearest primes: 1,637 (−1) · 1,657 (+19)

Divisors & multiples

All divisors (24)

1 · 2 · 3 · 6 · 7 · 9 · 13 · 14 · 18 · 21 · 26 · 39 · 42 · 63 · 78 · 91 · 117 · 126 · 182 · 234 · 273 · 546 · 819 (half) · 1638

Aliquot sum (sum of proper divisors): 2,730

Factor pairs (a × b = 1,638)

1 × 1638

2 × 819

3 × 546

6 × 273

7 × 234

9 × 182

13 × 126

14 × 117

18 × 91

21 × 78

26 × 63

39 × 42

First multiples

1,638 · 3,276 (double) · 4,914 · 6,552 · 8,190 · 9,828 · 11,466 · 13,104 · 14,742 · 16,380

Sums & aliquot sequence

As consecutive integers: 545 + 546 + 547 408 + 409 + 410 + 411 231 + 232 + … + 237 178 + 179 + … + 186

Aliquot sequence: 1,638 → 2,730 → 5,334 → 6,954 → 7,926 → 7,938 → 12,753 → 7,267 → 785 → 163 → 1 → 0 — terminates at zero

Continued fraction of √n

√1,638 = [40; (2, 8, 2, 80)]

Period length 4 — the block in parentheses repeats forever.

Representations

In words: one thousand six hundred thirty-eight
Ordinal: 1638th
Roman numeral: MDCXXXVIII
Binary: 11001100110
Octal: 3146
Hexadecimal: 0x666
Base64: BmY=
One's complement: 63,897 (16-bit)
Scientific notation: 1.638 × 10³
As a duration: 1,638 s = 27 minutes, 18 seconds

In other bases

ternary (3) 2020200

quaternary (4) 121212

quinary (5) 23023

senary (6) 11330

septenary (7) 4530

nonary (9) 2220

undecimal (11) 125a

duodecimal (12) b46

tridecimal (13) 990

tetradecimal (14) 850

pentadecimal (15) 743

Palindromic in base 16

As an angle

1,638° = 4 × 360° + 198°

198° ≈ 3.456 rad

Compass bearing: SSW (south-southwest)

Why does a circle have 360 degrees? →

Historical numeral systems

Babylonian (base 60): 𒌋𒌋𒁹𒁹𒁹𒁹𒁹𒁹𒁹 𒌋𒁹𒁹𒁹𒁹𒁹𒁹𒁹𒁹
Egyptian hieroglyphic: 𓆼𓍢𓍢𓍢𓍢𓍢𓍢𓎆𓎆𓎆𓏺𓏺𓏺𓏺𓏺𓏺𓏺𓏺
Greek (Milesian): ͵αχληʹ
Mayan (base 20): 𝋤·𝋡·𝋲
Chinese: 一千六百三十八
Chinese (financial): 壹仟陸佰參拾捌

In other modern scripts

Eastern Arabic ١٦٣٨ Devanagari १६३८ Bengali ১৬৩৮ Tamil ௧௬௩௮ Thai ๑๖๓๘ Tibetan ༡༦༣༨ Khmer ១៦៣៨ Lao ໑໖໓໘ Burmese ၁၆၃၈

Digit at this position in famous constants

π — Pi (π): Digit 1,638 = 4
e — Euler's number (e): Digit 1,638 = 1
φ — Golden ratio (φ): Digit 1,638 = 9
√2 — Pythagoras's (√2): Digit 1,638 = 9
ln 2 — Natural log of 2: Digit 1,638 = 3
γ — Euler-Mascheroni (γ): Digit 1,638 = 3

Also seen as

Goldbach decomposition

Goldbach's conjecture says every even integer greater than 2 is the sum of two primes. For 1638, here are decompositions:

11 + 1627 = 1638
17 + 1621 = 1638
19 + 1619 = 1638
29 + 1609 = 1638
31 + 1607 = 1638
37 + 1601 = 1638
41 + 1597 = 1638
59 + 1579 = 1638

Showing the first eight; more decompositions exist.

Unicode codepoint

Arabic-Indic Digit Six

U+0666

Decimal digit (Nd)

UTF-8 encoding: D9 A6 (2 bytes).

Lookup U+0666 on Compart ↗ Lookup on FileFormat.Info ↗

Hex color

#000666

RGB(0, 6, 102)

IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.0.6.102.

Address: 0.0.6.102
Class: reserved
IPv4-mapped IPv6: ::ffff:0.0.6.102

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

Musical pitch

Heard as a frequency, 1,638 Hz is closest to:

Concert pitch (A4 = 440 Hz): G♯6 (1661.2 Hz, -24¢)
Scientific pitch (C4 = 256 Hz): G♯6 (1625.5 Hz, +13¢)
Baroque pitch (A4 = 415 Hz): A6 (1660 Hz, -23¢)

Position in π

The digit sequence 1638 first appears in π at position 32,307 of the decimal expansion (the 32,307ordinal-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 1638 on Pi Search ↗