Live analysis

2,240

2,240 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.).

2,240 (two thousand two hundred forty) is an even 4-digit number. It is a composite number with 28 divisors, and factors as 2⁶ × 5 × 7. Its proper divisors sum to 3,856, more than the number itself, making it an abundant number. Written other ways, in Roman numerals it is MMCCXL and in binary, 100011000000.

Abundant Number Gapful Number Harshad / Niven Odious Number Pernicious Number Practical Number Recamán's Sequence Refactorable Number Semiperfect Number

Interestingness

★ ★ ★ ★ ☆

6 notable facts · grade B

2,228 2,229 2,230 2,231 2,232 2,233 2,234 2,235 2,236 2,237 2,238 2,239 2,240 2,241 2,242 2,243 2,244 2,245 2,246 2,247 2,248 2,249 2,250 2,251 2,252

less more

Properties

Parity: Even
Digit count: 4
Digit sum: 8
Digit product: 0
Digital root: 8
Palindrome: No
Bit width: 12 bits
Reversed: 422
Recamán's sequence: a(3,271) = 2,240
Square (n²): 5,017,600
Cube (n³): 11,239,424,000
Divisor count: 28
σ(n) — sum of divisors: 6,096
φ(n) — Euler's totient: 768
Sum of prime factors: 24

Primality

Prime factorization: 2 ⁶ × 5 × 7

Nearest primes: 2,239 (−1) · 2,243 (+3)

Divisors & multiples

All divisors (28)

1 · 2 · 4 · 5 · 7 · 8 · 10 · 14 · 16 · 20 · 28 · 32 · 35 · 40 · 56 · 64 · 70 · 80 · 112 · 140 · 160 · 224 · 280 · 320 · 448 · 560 · 1120 (half) · 2240

Aliquot sum (sum of proper divisors): 3,856

Factor pairs (a × b = 2,240)

1 × 2240

2 × 1120

4 × 560

5 × 448

7 × 320

8 × 280

10 × 224

14 × 160

16 × 140

20 × 112

28 × 80

32 × 70

35 × 64

40 × 56

First multiples

2,240 · 4,480 (double) · 6,720 · 8,960 · 11,200 · 13,440 · 15,680 · 17,920 · 20,160 · 22,400

Sums & aliquot sequence

As a sum of two cubes: 8³ + 12³

As consecutive integers: 446 + 447 + 448 + 449 + 450 317 + 318 + … + 323 47 + 48 + … + 81

Aliquot sequence: 2,240 → 3,856 → 3,646 → 1,826 → 1,198 → 602 → 454 → 230 → 202 → 104 → 106 → 56 → 64 → 63 → 41 → 1 → 0 — terminates at zero

Continued fraction of √n

√2,240 = [47; (3, 23, 3, 94)]

Period length 4 — the block in parentheses repeats forever.

Representations

In words: two thousand two hundred forty
Ordinal: 2240th
Roman numeral: MMCCXL
Binary: 100011000000
Octal: 4300
Hexadecimal: 0x8C0
Base64: CMA=
One's complement: 63,295 (16-bit)
Scientific notation: 2.24 × 10³
As a duration: 2,240 s = 37 minutes, 20 seconds

In other bases

ternary (3) 10001222

quaternary (4) 203000

quinary (5) 32430

senary (6) 14212

septenary (7) 6350

nonary (9) 3058

undecimal (11) 1757

duodecimal (12) 1368

tridecimal (13) 1034

tetradecimal (14) b60

pentadecimal (15) 9e5

As an angle

2,240° = 6 × 360° + 80°

80° ≈ 1.396 rad

Compass bearing: E (east)

Why does a circle have 360 degrees? →

Historical numeral systems

Babylonian (base 60): 𒌋𒌋𒌋𒁹𒁹𒁹𒁹𒁹𒁹𒁹 𒌋𒌋
Egyptian hieroglyphic: 𓆼𓆼𓍢𓍢𓎆𓎆𓎆𓎆
Greek (Milesian): ͵βσμʹ
Mayan (base 20): 𝋥·𝋬·𝋠
Chinese: 二千二百四十
Chinese (financial): 貳仟貳佰肆拾

In other modern scripts

Eastern Arabic ٢٢٤٠ Devanagari २२४० Bengali ২২৪০ Tamil ௨௨௪௦ Thai ๒๒๔๐ Tibetan ༢༢༤༠ Khmer ២២៤០ Lao ໒໒໔໐ Burmese ၂၂၄၀

Digit at this position in famous constants

π — Pi (π): Digit 2,240 = 0
e — Euler's number (e): Digit 2,240 = 9
φ — Golden ratio (φ): Digit 2,240 = 4
√2 — Pythagoras's (√2): Digit 2,240 = 4
ln 2 — Natural log of 2: Digit 2,240 = 4
γ — Euler-Mascheroni (γ): Digit 2,240 = 1

Also seen as

Goldbach decomposition

Goldbach's conjecture says every even integer greater than 2 is the sum of two primes. For 2240, here are decompositions:

3 + 2237 = 2240
19 + 2221 = 2240
37 + 2203 = 2240
61 + 2179 = 2240
79 + 2161 = 2240
97 + 2143 = 2240
103 + 2137 = 2240
109 + 2131 = 2240

Showing the first eight; more decompositions exist.

Unicode codepoint

ࣀ

Arabic Letter Tteh With Small V

U+08C0

Other letter (Lo)

UTF-8 encoding: E0 A3 80 (3 bytes).

Lookup U+08C0 on Compart ↗ Lookup on FileFormat.Info ↗

Hex color

#0008C0

RGB(0, 8, 192)

IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.0.8.192.

Address: 0.0.8.192
Class: reserved
IPv4-mapped IPv6: ::ffff:0.0.8.192

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

Musical pitch

Heard as a frequency, 2,240 Hz is closest to:

Concert pitch (A4 = 440 Hz): C♯7 (2217.5 Hz, +18¢)
Scientific pitch (C4 = 256 Hz): D7 (2298.8 Hz, -45¢ — about midway to C♯7)
Baroque pitch (A4 = 415 Hz): D7 (2215.8 Hz, +19¢)

Position in π

The digit sequence 2240 first appears in π at position 12,782 of the decimal expansion (the 12,782ordinal-suffix:nd 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 2240 on Pi Search ↗