Number

120

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

120 (one hundred twenty) is an even 3-digit number. It is a composite number with 16 divisors, and factors as 2³ × 3 × 5. Its proper divisors sum to 240, more than the number itself, making it an abundant number. It is the fifteenth triangular number and a factorial (5! = 120). Written other ways, in Roman numerals it is CXX and in binary, 1111000.

Abundant Number Evil Number Factorial Gapful Number Harshad / Niven Hexagonal Highly Abundant Highly Composite Number Practical Number Preferred Number Recamán's Sequence Semiperfect Number Tetrahedral Triangular Year

Interestingness

★ ★ ★ ★ ★

12 notable facts · grade A

108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132

less more

Historical context — 120 AD

Calendar year

Year 120 (CXX) was a leap year starting on Sunday of the Julian calendar.

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

Historical context — 120 BC

Calendar year

Year 120 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: 52
Started on: Monday
January 1, 120
Ended on: Tuesday
December 31, 120
Friday the 13ths: 2
2 Friday the 13ths this year.
Decade: 120s
120–129
Century: 2nd century
101–200
Millennium: 1st millennium
1–1000
Years ago: 1,906
1906 years before 2026.

In other calendars

Hebrew: 3880 / 3881 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: 663 BE
Counted from the parinirvana of the Buddha (Theravada / Thai / Sri Lankan convention).
Ethiopian: 112 / 113 ET
Year boundary at Enkutatash (September 11/12).
Indian National (Saka): 42 / 41 Saka
Indian national calendar; year starts in March.

Properties

Parity: Even
Digit count: 3
Digit sum: 3
Digit product: 0
Digital root: 3
Palindrome: No
Bit width: 7 bits
Reversed: 21
Recamán's sequence: a(160) = 120
Square (n²): 14,400
Cube (n³): 1,728,000
Divisor count: 16
σ(n) — sum of divisors: 360
φ(n) — Euler's totient: 32
Sum of prime factors: 14

Primality

Prime factorization: 2 ³ × 3 × 5

Nearest primes: 113 (−7) · 127 (+7)

Divisors & multiples

All divisors (16)

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

Aliquot sum (sum of proper divisors): 240

Factor pairs (a × b = 120)

1 × 120

2 × 60

3 × 40

4 × 30

5 × 24

6 × 20

8 × 15

10 × 12

First multiples

120 · 240 (double) · 360 · 480 · 600 · 720 · 840 · 960 · 1,080 · 1,200

Sums & aliquot sequence

As consecutive integers: 39 + 40 + 41 22 + 23 + 24 + 25 + 26 1 + 2 + … + 15

Aliquot sequence: 120 → 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

√120 = [10; (1, 20)]

Period length 2 — the block in parentheses repeats forever.

Representations

In words: one hundred twenty
Ordinal: 120th
Roman numeral: CXX
Binary: 1111000
Octal: 170
Hexadecimal: 0x78
Base64: eA==
One's complement: 135 (8-bit)
Scientific notation: 1.2 × 10²
As a duration: 120 s = 2 minutes

In other bases

ternary (3) 11110

quaternary (4) 1320

quinary (5) 440

senary (6) 320

septenary (7) 231

nonary (9) 143

undecimal (11) aa

duodecimal (12) a0

tridecimal (13) 93

tetradecimal (14) 88

pentadecimal (15) 80

As an angle

120°

120° ≈ 2.094 rad

Compass bearing: ESE (east-southeast)

Why does a circle have 360 degrees? →

Historical numeral systems

Babylonian (base 60): 𒁹𒁹 ·
Egyptian hieroglyphic: 𓍢𓎆𓎆
Greek (Milesian): ρκʹ
Mayan (base 20): 𝋦·𝋠
Chinese: 一百二十
Chinese (financial): 壹佰貳拾

In other modern scripts

Eastern Arabic ١٢٠ Devanagari १२० Bengali ১২০ Tamil ௧௨௦ Thai ๑๒๐ Tibetan ༡༢༠ Khmer ១២០ Lao ໑໒໐ Burmese ၁၂၀

Digit at this position in famous constants

π — Pi (π): Digit 120 = 4
e — Euler's number (e): Digit 120 = 2
φ — Golden ratio (φ): Digit 120 = 5
√2 — Pythagoras's (√2): Digit 120 = 2
ln 2 — Natural log of 2: Digit 120 = 3
γ — Euler-Mascheroni (γ): Digit 120 = 8

Also seen as

Goldbach decomposition

Goldbach's conjecture says every even integer greater than 2 is the sum of two primes. For 120, here are decompositions:

7 + 113 = 120
11 + 109 = 120
13 + 107 = 120
17 + 103 = 120
19 + 101 = 120
23 + 97 = 120
31 + 89 = 120
37 + 83 = 120

Showing the first eight; more decompositions exist.

ASCII character

As an ASCII codepoint, 120 is x. Printable ASCII character x.

Hex color

#000078

RGB(0, 0, 120)

IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.0.0.120.

Address: 0.0.0.120
Class: reserved
IPv4-mapped IPv6: ::ffff:0.0.0.120

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

Musical pitch

Heard as a frequency, 120 Hz is closest to:

Concert pitch (A4 = 440 Hz): B2 (123.5 Hz, -49¢ — about midway to A♯2)
Scientific pitch (C4 = 256 Hz): B2 (120.8 Hz, -12¢)
Baroque pitch (A4 = 415 Hz): C3 (123.4 Hz, -48¢ — about midway to B2)

As a MIDI note number, 120 is C9 (8372 Hz at concert pitch).

Food additive (E-number)

On an ingredients label, E120 is Cochineal / carmine, a food colour — a crimson made from crushed cochineal insects.

E-number reference (Wikipedia) ↗

Angle

120° is 2π/3 radians — the interior angle of a regular hexagon.