Number

1,340

1,340 is a composite number, even, a calendar year.

1,340 (one thousand three hundred forty) is an even 4-digit number. It is a composite number with 12 divisors, and factors as 2² × 5 × 67. Its proper divisors sum to 1,516, more than the number itself, making it an abundant number. Written other ways, in Roman numerals it is MCCCXL and in binary, 10100111100.

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

Interestingness

★ ★ ★ ☆ ☆

5 notable facts · grade C

1,328 1,329 1,330 1,331 1,332 1,333 1,334 1,335 1,336 1,337 1,338 1,339 1,340 1,341 1,342 1,343 1,344 1,345 1,346 1,347 1,348 1,349 1,350 1,351 1,352

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Historical context — 1340 AD

Calendar year

Year 1340 (MCCCXL) was a leap year starting on Saturday of the Julian calendar.

Excerpt from Wikipedia (en) ↗ · Licensed CC BY-SA 4.0 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: Friday
January 1, 1340
Ended on: Saturday
December 31, 1340
Friday the 13ths: 1
One Friday the 13th this year.
Decade: 1340s
1340–1349
Century: 14th century
1301–1400
Millennium: 2nd millennium
1001–2000
Years ago: 686
686 years before 2026.

In other calendars

Hebrew: 5100 / 5101 AM
Rosh Hashanah falls in September/October.
Islamic Hijri: 740 / 741 AH
Lunar calendar; year spans differ from Gregorian.
Chinese: Year of the zodiac:Metal zodiac:Dragon
Sexagenary cycle position 17 of 60. Lunar new year falls in late January / mid-February.
Buddhist Era: 1883 BE
Counted from the parinirvana of the Buddha (Theravada / Thai / Sri Lankan convention).
Persian Solar Hijri: 718 / 719 SH
Iranian calendar; Nowruz (new year) falls on the spring equinox.
Ethiopian: 1332 / 1333 ET
Year boundary at Enkutatash (September 11/12).
Indian National (Saka): 1262 / 1261 Saka
Indian national calendar; year starts in March.

Properties

Parity: Even
Digit count: 4
Digit sum: 8
Digit product: 0
Digital root: 8
Palindrome: No
Bit width: 11 bits
Reversed: 431
Recamán's sequence: a(16,455) = 1,340
Square (n²): 1,795,600
Cube (n³): 2,406,104,000
Divisor count: 12
σ(n) — sum of divisors: 2,856
φ(n) — Euler's totient: 528
Sum of prime factors: 76

Primality

Prime factorization: 2 ² × 5 × 67

Nearest primes: 1,327 (−13) · 1,361 (+21)

Divisors & multiples

All divisors (12)

1 · 2 · 4 · 5 · 10 · 20 · 67 · 134 · 268 · 335 · 670 (half) · 1340

Aliquot sum (sum of proper divisors): 1,516

Factor pairs (a × b = 1,340)

1 × 1340

2 × 670

4 × 335

5 × 268

10 × 134

20 × 67

First multiples

1,340 · 2,680 (double) · 4,020 · 5,360 · 6,700 · 8,040 · 9,380 · 10,720 · 12,060 · 13,400

Sums & aliquot sequence

As consecutive integers: 266 + 267 + 268 + 269 + 270 164 + 165 + … + 171 14 + 15 + … + 53

Aliquot sequence: 1,340 → 1,516 → 1,144 → 1,376 → 1,396 → 1,054 → 674 → 340 → 416 → 466 → 236 → 184 → 176 → 196 → 203 → 37 → 1 — unresolved within range

Continued fraction of √n

√1,340 = [36; (1, 1, 1, 1, 6, 18, 6, 1, 1, 1, 1, 72)]

Period length 12 — the block in parentheses repeats forever.

Representations

In words: one thousand three hundred forty
Ordinal: 1340th
Roman numeral: MCCCXL
Binary: 10100111100
Octal: 2474
Hexadecimal: 0x53C
Base64: BTw=
One's complement: 64,195 (16-bit)
Scientific notation: 1.34 × 10³
As a duration: 1,340 s = 22 minutes, 20 seconds

In other bases

ternary (3) 1211122

quaternary (4) 110330

quinary (5) 20330

senary (6) 10112

septenary (7) 3623

nonary (9) 1748

undecimal (11) 1009

duodecimal (12) 938

tridecimal (13) 7c1

tetradecimal (14) 6ba

pentadecimal (15) 5e5

Palindromic in base 15

As an angle

1,340° = 3 × 360° + 260°

260° ≈ 4.538 rad

Compass bearing: W (west)

Why does a circle have 360 degrees? →

Historical numeral systems

Babylonian (base 60): 𒌋𒌋𒁹𒁹 𒌋𒌋
Egyptian hieroglyphic: 𓆼𓍢𓍢𓍢𓎆𓎆𓎆𓎆
Greek (Milesian): ͵ατμʹ
Mayan (base 20): 𝋣·𝋧·𝋠
Chinese: 一千三百四十
Chinese (financial): 壹仟參佰肆拾

In other modern scripts

Eastern Arabic ١٣٤٠ Devanagari १३४० Bengali ১৩৪০ Tamil ௧௩௪௦ Thai ๑๓๔๐ Tibetan ༡༣༤༠ Khmer ១៣៤០ Lao ໑໓໔໐ Burmese ၁၃၄၀

Digit at this position in famous constants

π — Pi (π): Digit 1,340 = 0
e — Euler's number (e): Digit 1,340 = 7
φ — Golden ratio (φ): Digit 1,340 = 0
√2 — Pythagoras's (√2): Digit 1,340 = 6
ln 2 — Natural log of 2: Digit 1,340 = 3
γ — Euler-Mascheroni (γ): Digit 1,340 = 8

Also seen as

Goldbach decomposition

Goldbach's conjecture says every even integer greater than 2 is the sum of two primes. For 1340, here are decompositions:

13 + 1327 = 1340
19 + 1321 = 1340
37 + 1303 = 1340
43 + 1297 = 1340
61 + 1279 = 1340
103 + 1237 = 1340
109 + 1231 = 1340
127 + 1213 = 1340

Showing the first eight; more decompositions exist.

Unicode codepoint

Armenian Capital Letter Liwn

U+053C

Uppercase letter (Lu)

UTF-8 encoding: D4 BC (2 bytes).

Lookup U+053C on Compart ↗ Lookup on FileFormat.Info ↗

Hex color

#00053C

RGB(0, 5, 60)

IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.0.5.60.

Address: 0.0.5.60
Class: reserved
IPv4-mapped IPv6: ::ffff:0.0.5.60

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

Musical pitch

Heard as a frequency, 1,340 Hz is closest to:

Concert pitch (A4 = 440 Hz): E6 (1318.5 Hz, +28¢)
Scientific pitch (C4 = 256 Hz): F6 (1366.9 Hz, -34¢)
Baroque pitch (A4 = 415 Hz): F6 (1317.5 Hz, +29¢)

Position in π

The digit sequence 1340 first appears in π at position 5,512 of the decimal expansion (the 5,512ordinal-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 1340 on Pi Search ↗