Live analysis

2,140

2,140 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.).

2,140 (two thousand one hundred forty) is an even 4-digit number. It is a composite number with 12 divisors, and factors as 2² × 5 × 107. Its proper divisors sum to 2,396, more than the number itself, making it an abundant number. Written other ways, in Roman numerals it is MMCXL and in binary, 100001011100.

Abundant Number Arithmetic Number Cube-Free Gapful Number Odious Number Pernicious Number Recamán's Sequence Semiperfect Number

Interestingness

★ ★ ★ ☆ ☆

5 notable facts · grade C

2,128 2,129 2,130 2,131 2,132 2,133 2,134 2,135 2,136 2,137 2,138 2,139 2,140 2,141 2,142 2,143 2,144 2,145 2,146 2,147 2,148 2,149 2,150 2,151 2,152

less more

Properties

Parity: Even
Digit count: 4
Digit sum: 7
Digit product: 0
Digital root: 7
Palindrome: No
Bit width: 12 bits
Reversed: 412
Recamán's sequence: a(3,471) = 2,140
Square (n²): 4,579,600
Cube (n³): 9,800,344,000
Divisor count: 12
σ(n) — sum of divisors: 4,536
φ(n) — Euler's totient: 848
Sum of prime factors: 116

Primality

Prime factorization: 2 ² × 5 × 107

Nearest primes: 2,137 (−3) · 2,141 (+1)

Divisors & multiples

All divisors (12)

1 · 2 · 4 · 5 · 10 · 20 · 107 · 214 · 428 · 535 · 1070 (half) · 2140

Aliquot sum (sum of proper divisors): 2,396

Factor pairs (a × b = 2,140)

1 × 2140

2 × 1070

4 × 535

5 × 428

10 × 214

20 × 107

First multiples

2,140 · 4,280 (double) · 6,420 · 8,560 · 10,700 · 12,840 · 14,980 · 17,120 · 19,260 · 21,400

Sums & aliquot sequence

As consecutive integers: 426 + 427 + 428 + 429 + 430 264 + 265 + … + 271 34 + 35 + … + 73

Aliquot sequence: 2,140 → 2,396 → 1,804 → 1,724 → 1,300 → 1,738 → 1,142 → 574 → 434 → 334 → 170 → 154 → 134 → 70 → 74 → 40 → 50 — unresolved within range

Continued fraction of √n

√2,140 = [46; (3, 1, 5, 2, 2, 1, 1, 9, 1, 2, 3, 1, 1, 22, 1, 1, 3, 2, 1, 9, 1, 1, 2, 2, …)]

Period length 28 — the block in parentheses repeats forever.

Representations

In words: two thousand one hundred forty
Ordinal: 2140th
Roman numeral: MMCXL
Binary: 100001011100
Octal: 4134
Hexadecimal: 0x85C
Base64: CFw=
One's complement: 63,395 (16-bit)
Scientific notation: 2.14 × 10³
As a duration: 2,140 s = 35 minutes, 40 seconds

In other bases

ternary (3) 2221021

quaternary (4) 201130

quinary (5) 32030

senary (6) 13524

septenary (7) 6145

nonary (9) 2837

undecimal (11) 1676

duodecimal (12) 12a4

tridecimal (13) c88

tetradecimal (14) acc

pentadecimal (15) 97a

As an angle

2,140° = 5 × 360° + 340°

340° ≈ 5.934 rad

Compass bearing: NNW (north-northwest)

Why does a circle have 360 degrees? →

Historical numeral systems

Babylonian (base 60): 𒌋𒌋𒌋𒁹𒁹𒁹𒁹𒁹 𒌋𒌋𒌋𒌋
Egyptian hieroglyphic: 𓆼𓆼𓍢𓎆𓎆𓎆𓎆
Greek (Milesian): ͵βρμʹ
Mayan (base 20): 𝋥·𝋧·𝋠
Chinese: 二千一百四十
Chinese (financial): 貳仟壹佰肆拾

In other modern scripts

Eastern Arabic ٢١٤٠ Devanagari २१४० Bengali ২১৪০ Tamil ௨௧௪௦ Thai ๒๑๔๐ Tibetan ༢༡༤༠ Khmer ២១៤០ Lao ໒໑໔໐ Burmese ၂၁၄၀

Digit at this position in famous constants

π — Pi (π): Digit 2,140 = 7
e — Euler's number (e): Digit 2,140 = 1
φ — Golden ratio (φ): Digit 2,140 = 8
√2 — Pythagoras's (√2): Digit 2,140 = 3
ln 2 — Natural log of 2: Digit 2,140 = 5
γ — Euler-Mascheroni (γ): Digit 2,140 = 6

Also seen as

Goldbach decomposition

Goldbach's conjecture says every even integer greater than 2 is the sum of two primes. For 2140, here are decompositions:

3 + 2137 = 2140
11 + 2129 = 2140
29 + 2111 = 2140
41 + 2099 = 2140
53 + 2087 = 2140
59 + 2081 = 2140
71 + 2069 = 2140
101 + 2039 = 2140

Showing the first eight; more decompositions exist.

Hex color

#00085C

RGB(0, 8, 92)

IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.0.8.92.

Address: 0.0.8.92
Class: reserved
IPv4-mapped IPv6: ::ffff:0.0.8.92

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

Musical pitch

Heard as a frequency, 2,140 Hz is closest to:

Concert pitch (A4 = 440 Hz): C7 (2093 Hz, +38¢)
Scientific pitch (C4 = 256 Hz): C♯7 (2169.8 Hz, -24¢)
Baroque pitch (A4 = 415 Hz): C♯7 (2091.5 Hz, +40¢)

Position in π

The digit sequence 2140 first appears in π at position 8,433 of the decimal expansion (the 8,433ordinal-suffix:rd 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 2140 on Pi Search ↗