Number

90

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

90 (ninety) is an even 2-digit number. It is a composite number with 12 divisors, and factors as 2 × 3² × 5. Its proper divisors sum to 144, more than the number itself, making it an abundant number. Written other ways, in Roman numerals it is XC and in binary, 1011010.

Abundant Number Cube-Free Evil Number Flippable Harshad / Niven Highly Abundant Perrin Number Practical Number Pronic / Oblong Recamán's Sequence Semiperfect Number Year

Interestingness

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9 notable facts · grade A

78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102

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Historical context — 90 AD

Calendar year

AD 90 (XC) was a common year starting on Friday of the Julian calendar.

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

Historical context — 90 BC

Calendar year

Year 90 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: Common year
Standard 365-day year; not divisible by 4 (or divisible by 100 but not 400).
Days in year: 365
ISO weeks: 52
Started on: Sunday
January 1, 90
Ended on: Sunday
December 31, 90
Friday the 13ths: 2
2 Friday the 13ths this year.
Decade: 90s
90–99
Century: 1st century
1–100
Millennium: 1st millennium
1–1000
Years ago: 1,936
1936 years before 2026.

In other calendars

Hebrew: 3850 / 3851 AM
Rosh Hashanah falls in September/October.
Chinese: Year of the zodiac:Metal zodiac:Tiger
Sexagenary cycle position 27 of 60. Lunar new year falls in late January / mid-February.
Buddhist Era: 633 BE
Counted from the parinirvana of the Buddha (Theravada / Thai / Sri Lankan convention).
Ethiopian: 82 / 83 ET
Year boundary at Enkutatash (September 11/12).
Indian National (Saka): 12 / 11 Saka
Indian national calendar; year starts in March.

Properties

Parity: Even
Digit count: 2
Digit sum: 9
Digit product: 0
Digital root: 9
Palindrome: No
Bit width: 7 bits
Reversed: 9
Flips to (rotate 180°): 6
Recamán's sequence: a(63) = 90
Square (n²): 8,100
Cube (n³): 729,000
Divisor count: 12
σ(n) — sum of divisors: 234
φ(n) — Euler's totient: 24
Sum of prime factors: 13

Primality

Prime factorization: 2 × 3 ² × 5

Nearest primes: 89 (−1) · 97 (+7)

Divisors & multiples

All divisors (12)

1 · 2 · 3 · 5 · 6 · 9 · 10 · 15 · 18 · 30 · 45 (half) · 90

Aliquot sum (sum of proper divisors): 144

Factor pairs (a × b = 90)

1 × 90

2 × 45

3 × 30

5 × 18

6 × 15

9 × 10

First multiples

90 · 180 (double) · 270 · 360 · 450 · 540 · 630 · 720 · 810 · 900

Sums & aliquot sequence

As a sum of two squares: 3² + 9²

As consecutive integers: 29 + 30 + 31 21 + 22 + 23 + 24 16 + 17 + 18 + 19 + 20 6 + 7 + … + 14

Aliquot sequence: 90 → 144 → 259 → 45 → 33 → 15 → 9 → 4 → 3 → 1 → 0 — terminates at zero

Continued fraction of √n

√90 = [9; (2, 18)]

Period length 2 — the block in parentheses repeats forever.

Representations

In words: ninety
Ordinal: 90th
Roman numeral: XC
Binary: 1011010
Octal: 132
Hexadecimal: 0x5A
Base64: Wg==
One's complement: 165 (8-bit)
Scientific notation: 9 × 10¹
As a duration: 90 s = 1 minute, 30 seconds

In other bases

ternary (3) 10100

quaternary (4) 1122

quinary (5) 330

senary (6) 230

septenary (7) 156

nonary (9) 110

undecimal (11) 82

duodecimal (12) 76

tridecimal (13) 6c

tetradecimal (14) 66

pentadecimal (15) 60

As an angle

90°

90° ≈ 1.571 rad

Compass bearing: E (east)

Why does a circle have 360 degrees? →

Historical numeral systems

Babylonian (base 60): 𒁹 𒌋𒌋𒌋
Egyptian hieroglyphic: 𓎆𓎆𓎆𓎆𓎆𓎆𓎆𓎆𓎆
Greek (Milesian): ϟʹ
Mayan (base 20): 𝋤·𝋪
Chinese: 九十
Chinese (financial): 玖拾

In other modern scripts

Eastern Arabic ٩٠ Devanagari ९० Bengali ৯০ Tamil ௯௦ Thai ๙๐ Tibetan ༩༠ Khmer ៩០ Lao ໙໐ Burmese ၉၀

Digit at this position in famous constants

π — Pi (π): Digit 90 = 2
e — Euler's number (e): Digit 90 = 7
φ — Golden ratio (φ): Digit 90 = 0
√2 — Pythagoras's (√2): Digit 90 = 3
ln 2 — Natural log of 2: Digit 90 = 2
γ — Euler-Mascheroni (γ): Digit 90 = 6

Also seen as

Goldbach decomposition

Goldbach's conjecture says every even integer greater than 2 is the sum of two primes. For 90, here are decompositions:

7 + 83 = 90
11 + 79 = 90
17 + 73 = 90
19 + 71 = 90
23 + 67 = 90
29 + 61 = 90
31 + 59 = 90
37 + 53 = 90

Showing the first eight; more decompositions exist.

ASCII character

As an ASCII codepoint, 90 is Z. Printable ASCII character Z.

Hex color

#00005A

RGB(0, 0, 90)

IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.0.0.90.

Address: 0.0.0.90
Class: reserved
IPv4-mapped IPv6: ::ffff:0.0.0.90

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

US numbered highway

Matches numbered highway designation:

I-90 — Seattle, WA to Boston, MA — the longest Interstate (3,020 mi).

Interstate 90 on Wikipedia ↗

Geographic coordinate

As a geographic coordinate in degrees, this matches:

Pole (latitude) — 90° latitude — the North Pole (90°N) and South Pole (90°S).

World map (equirectangular projection) — Latitude 90° — Pole

Musical pitch

Heard as a frequency, 90 Hz is closest to:

Concert pitch (A4 = 440 Hz): F♯2 (92.5 Hz, -47¢ — about midway to F2)
Scientific pitch (C4 = 256 Hz): F♯2 (90.5 Hz, -10¢)
Baroque pitch (A4 = 415 Hz): G2 (92.4 Hz, -46¢ — about midway to F♯2)

(very low — many laptop and phone speakers can't reproduce it)

As a MIDI note number, 90 is F♯6 (1480 Hz at concert pitch).

Atomic number

On the periodic table, atomic number 90 is Thorium (Th) — period 7.

Thorium on Wikipedia ↗

Angle

90° is π/2 radians — a right angle.