Number

840

840 is a composite number, even, a calendar year.

Abundant Number Arithmetic Number Descending Digits Evil Number Harshad / Niven Practical Number Recamán's Sequence Semiperfect Number Stepped Digits Year

Historical context — 840 AD

Calendar year

Year 840 (DCCCXL) was a leap year starting on Thursday in the Julian calendar, the 840th year of the Common Era (CE) and Anno Domini (AD) designations, the 840th year of the 1st millennium, the 40th year of the 9th century, and the 1st year of the 840s decade.

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

Historical context — 840 BC

Decade

This article concerns the period 849 BC – 840 BC.

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

Year facts

Year type: Leap year
Divisible by 4 and not by 100; February has 29 days.
Days in year: 366
ISO weeks: 52
Started on: Sunday
January 1, 840
Ended on: Monday
December 31, 840
Friday the 13ths: 3
3 Friday the 13ths this year.
Decade: 840s
840–849
Century: 9th century
801–900
Millennium: 1st millennium
1–1000
Years ago: 1,186
1186 years before 2026.

In other calendars

Hebrew: 4600 / 4601 AM
Rosh Hashanah falls in September/October.
Islamic Hijri: 225 / 226 AH
Lunar calendar; year spans differ from Gregorian.
Chinese: Year of the zodiac:Metal zodiac:Monkey
Sexagenary cycle position 57 of 60. Lunar new year falls in late January / mid-February.
Buddhist Era: 1383 BE
Counted from the parinirvana of the Buddha (Theravada / Thai / Sri Lankan convention).
Persian Solar Hijri: 218 / 219 SH
Iranian calendar; Nowruz (new year) falls on the spring equinox.
Ethiopian: 832 / 833 ET
Year boundary at Enkutatash (September 11/12).
Indian National (Saka): 762 / 761 Saka
Indian national calendar; year starts in March.

Properties

Parity: Even
Digit count: 3
Digit sum: 12
Digit product: 0
Digital root: 3
Palindrome: No
Bit width: 10 bits
Reversed: 48
Recamán's sequence: a(343) = 840
Square (n²): 705,600
Cube (n³): 592,704,000
Divisor count: 32
σ(n) — sum of divisors: 2,880
φ(n) — Euler's totient: 192
Sum of prime factors: 21

Primality

Prime factorization: 2 ³ × 3 × 5 × 7

Nearest primes: 839 (−1) · 853 (+13)

Divisors & multiples

All divisors (32)

1 · 2 · 3 · 4 · 5 · 6 · 7 · 8 · 10 · 12 · 14 · 15 · 20 · 21 · 24 · 28 · 30 · 35 · 40 · 42 · 56 · 60 · 70 · 84 · 105 · 120 · 140 · 168 · 210 · 280 · 420 (half) · 840

Aliquot sum (sum of proper divisors): 2,040

Factor pairs (a × b = 840)

1 × 840

2 × 420

3 × 280

4 × 210

5 × 168

6 × 140

7 × 120

8 × 105

10 × 84

12 × 70

14 × 60

15 × 56

20 × 42

21 × 40

24 × 35

28 × 30

First multiples

840 · 1,680 (double) · 2,520 · 3,360 · 4,200 · 5,040 · 5,880 · 6,720 · 7,560 · 8,400

Sums & aliquot sequence

As consecutive integers: 279 + 280 + 281 166 + 167 + 168 + 169 + 170 117 + 118 + … + 123 49 + 50 + … + 63

Aliquot sequence: 840 → 2,040 → 4,440 → 9,240 → 25,320 → 51,000 → 117,480 → 271,320 → 765,480 → 1,531,320 → 3,721,800 → 7,817,640 → 15,635,640 → 32,899,560 → 65,799,480 → 139,098,120 → 349,027,320 — unresolved within range

Representations

In words: eight hundred forty
Ordinal: 840th
Roman numeral: DCCCXL
Binary: 1101001000
Octal: 1510
Hexadecimal: 0x348
Base64: A0g=
One's complement: 64,695 (16-bit)

In other bases

ternary (3) 1011010

quaternary (4) 31020

quinary (5) 11330

senary (6) 3520

septenary (7) 2310

nonary (9) 1133

undecimal (11) 6a4

duodecimal (12) 5a0

tridecimal (13) 4c8

tetradecimal (14) 440

pentadecimal (15) 3b0

Historical numeral systems

Babylonian (base 60): 𒌋𒁹𒁹𒁹𒁹 ·
Egyptian hieroglyphic: 𓍢𓍢𓍢𓍢𓍢𓍢𓍢𓍢𓎆𓎆𓎆𓎆
Greek (Milesian): ωμʹ
Mayan (base 20): 𝋢·𝋢·𝋠
Chinese: 八百四十
Chinese (financial): 捌佰肆拾

In other modern scripts

Eastern Arabic ٨٤٠ Devanagari ८४० Bengali ৮৪০ Tamil ௮௪௦ Thai ๘๔๐ Tibetan ༨༤༠ Khmer ៨៤០ Lao ໘໔໐ Burmese ၈၄၀

Digit at this position in famous constants

π — Pi (π): Digit 840 = 3
e — Euler's number (e): Digit 840 = 3
φ — Golden ratio (φ): Digit 840 = 8
√2 — Pythagoras's (√2): Digit 840 = 6
ln 2 — Natural log of 2: Digit 840 = 7
γ — Euler-Mascheroni (γ): Digit 840 = 5

Also seen as

Goldbach decomposition

Goldbach's conjecture says every even integer greater than 2 is the sum of two primes. For 840, here are decompositions:

11 + 829 = 840
13 + 827 = 840
17 + 823 = 840
19 + 821 = 840
29 + 811 = 840
31 + 809 = 840
43 + 797 = 840
53 + 787 = 840

Showing the first eight; more decompositions exist.

Unicode codepoint

Combining Double Vertical Line Below

U+0348

Non-spacing mark (Mn)

UTF-8 encoding: CD 88 (2 bytes).

Lookup U+0348 on Compart ↗ Lookup on FileFormat.Info ↗

Hex color

#000348

RGB(0, 3, 72)

IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.0.3.72.

Address: 0.0.3.72
Class: reserved
IPv4-mapped IPv6: ::ffff:0.0.3.72

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