Number

240

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

240 (two hundred forty) is an even 3-digit number. It is a composite number with 20 divisors, and factors as 2⁴ × 3 × 5. Its proper divisors sum to 504, more than the number itself, making it an abundant number. Written other ways, in Roman numerals it is CCXL and in binary, 11110000.

Abundant Number Evil Number Gapful Number Harshad / Niven Highly Abundant Highly Composite Number Practical Number Preferred Number Pronic / Oblong Recamán's Sequence Refactorable Number Semiperfect Number Year

Interestingness

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10 notable facts · grade A

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Historical context — 240 AD

Calendar year

Year 240 (CCXL) was a leap year starting on Wednesday of the Julian calendar.

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

Historical context — 240 BC

Calendar year

Year 240 BC was a year of the pre-Julian Roman 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: 53
Long year: contains 53 ISO weeks.
Started on: Wednesday
January 1, 240
Ended on: Thursday
December 31, 240
Friday the 13ths: 2
2 Friday the 13ths this year.
Decade: 240s
240–249
Century: 3rd century
201–300
Millennium: 1st millennium
1–1000
Years ago: 1,786
1786 years before 2026.

In other calendars

Hebrew: 4000 / 4001 AM
Rosh Hashanah falls in September/October.
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: 783 BE
Counted from the parinirvana of the Buddha (Theravada / Thai / Sri Lankan convention).
Ethiopian: 232 / 233 ET
Year boundary at Enkutatash (September 11/12).
Indian National (Saka): 162 / 161 Saka
Indian national calendar; year starts in March.

Properties

Parity: Even
Digit count: 3
Digit sum: 6
Digit product: 0
Digital root: 6
Palindrome: No
Bit width: 8 bits
Reversed: 42
Recamán's sequence: a(263) = 240
Square (n²): 57,600
Cube (n³): 13,824,000
Divisor count: 20
σ(n) — sum of divisors: 744
φ(n) — Euler's totient: 64
Sum of prime factors: 16

Primality

Prime factorization: 2 ⁴ × 3 × 5

Nearest primes: 239 (−1) · 241 (+1)

Divisors & multiples

All divisors (20)

1 · 2 · 3 · 4 · 5 · 6 · 8 · 10 · 12 · 15 · 16 · 20 · 24 · 30 · 40 · 48 · 60 · 80 · 120 (half) · 240

Aliquot sum (sum of proper divisors): 504

Factor pairs (a × b = 240)

1 × 240

2 × 120

3 × 80

4 × 60

5 × 48

6 × 40

8 × 30

10 × 24

12 × 20

15 × 16

First multiples

240 · 480 (double) · 720 · 960 · 1,200 · 1,440 · 1,680 · 1,920 · 2,160 · 2,400

Sums & aliquot sequence

As consecutive integers: 79 + 80 + 81 46 + 47 + 48 + 49 + 50 9 + 10 + … + 23

Aliquot sequence: 240 → 504 → 1,056 → 1,968 → 3,240 → 7,650 → 14,112 → 32,571 → 27,333 → 12,161 → 1 → 0 — terminates at zero

Continued fraction of √n

√240 = [15; (2, 30)]

Period length 2 — the block in parentheses repeats forever.

Representations

In words: two hundred forty
Ordinal: 240th
Roman numeral: CCXL
Binary: 11110000
Octal: 360
Hexadecimal: 0xF0
Base64: 8A==
One's complement: 15 (8-bit)
Scientific notation: 2.4 × 10²
As a duration: 240 s = 4 minutes

In other bases

ternary (3) 22220

quaternary (4) 3300

quinary (5) 1430

senary (6) 1040

septenary (7) 462

nonary (9) 286

undecimal (11) 1a9

duodecimal (12) 180

tridecimal (13) 156

tetradecimal (14) 132

pentadecimal (15) 110

As an angle

240°

240° ≈ 4.189 rad

Compass bearing: WSW (west-southwest)

Why does a circle have 360 degrees? →

Historical numeral systems

Babylonian (base 60): 𒁹𒁹𒁹𒁹 ·
Egyptian hieroglyphic: 𓍢𓍢𓎆𓎆𓎆𓎆
Greek (Milesian): σμʹ
Mayan (base 20): 𝋬·𝋠
Chinese: 二百四十
Chinese (financial): 貳佰肆拾

In other modern scripts

Eastern Arabic ٢٤٠ Devanagari २४० Bengali ২৪০ Tamil ௨௪௦ Thai ๒๔๐ Tibetan ༢༤༠ Khmer ២៤០ Lao ໒໔໐ Burmese ၂၄၀

Digit at this position in famous constants

π — Pi (π): Digit 240 = 6
e — Euler's number (e): Digit 240 = 4
φ — Golden ratio (φ): Digit 240 = 6
√2 — Pythagoras's (√2): Digit 240 = 1
ln 2 — Natural log of 2: Digit 240 = 5
γ — Euler-Mascheroni (γ): Digit 240 = 2

Also seen as

Goldbach decomposition

Goldbach's conjecture says every even integer greater than 2 is the sum of two primes. For 240, here are decompositions:

7 + 233 = 240
11 + 229 = 240
13 + 227 = 240
17 + 223 = 240
29 + 211 = 240
41 + 199 = 240
43 + 197 = 240
47 + 193 = 240

Showing the first eight; more decompositions exist.

Unicode codepoint

Latin Small Letter Eth

U+00F0

Lowercase letter (Ll)

UTF-8 encoding: C3 B0 (2 bytes).

Lookup U+00F0 on Compart ↗ Lookup on FileFormat.Info ↗

Hex color

#0000F0

RGB(0, 0, 240)

IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.0.0.240.

Address: 0.0.0.240
Class: reserved
IPv4-mapped IPv6: ::ffff:0.0.0.240

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

NANP area code 240

The number 240 is an active NANP area code (North American Numbering Plan).

Primary area: Western suburbs of D.C.
Region: Maryland
Country: United States

Most NANP area codes have multiple overlays in dense regions; the primary area listed is the historic/largest population center for this code.

Look up area code 240 ↗

Musical pitch

Heard as a frequency, 240 Hz is closest to:

Concert pitch (A4 = 440 Hz): B3 (246.9 Hz, -49¢ — about midway to A♯3)
Scientific pitch (C4 = 256 Hz): B3 (241.6 Hz, -12¢)
Baroque pitch (A4 = 415 Hz): C4 (246.8 Hz, -48¢ — about midway to B3)