Number

45

45 is a composite number, odd, a calendar year.

45 (forty-five) is an odd 2-digit number. It is a composite number with 6 divisors, and factors as 3² × 5. It is the ninth triangular number. Written other ways, in Roman numerals it is XLV and in binary, 101101.

Arithmetic Number Binary Palindrome Cube-Free Deficient Number Evil Number Harshad / Niven Hexagonal Kaprekar Number Moran Number Recamán's Sequence Triangular Year

Interestingness

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9 notable facts · grade A

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Historical context — 45 AD

Calendar year

AD 45 (XLV) 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 — 45 BC

Calendar year

Year 45 BC was either a common year starting on Thursday, Friday or Saturday or a leap year starting on Friday or Saturday and the first year of the Julian calendar and a leap year starting on Friday of the Proleptic Julian 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, 45
Ended on: Sunday
December 31, 45
Friday the 13ths: 2
2 Friday the 13ths this year.
Decade: 40s
40–49
Century: 1st century
1–100
Millennium: 1st millennium
1–1000
Years ago: 1,981
1981 years before 2026.

In other calendars

Hebrew: 3805 / 3806 AM
Rosh Hashanah falls in September/October.
Chinese: Year of the zodiac:Wood zodiac:Snake
Sexagenary cycle position 42 of 60. Lunar new year falls in late January / mid-February.
Buddhist Era: 588 BE
Counted from the parinirvana of the Buddha (Theravada / Thai / Sri Lankan convention).
Ethiopian: 37 / 38 ET
Year boundary at Enkutatash (September 11/12).
Indian National (Saka): -33 / -34 Saka
Indian national calendar; year starts in March.

Properties

Parity: Odd
Digit count: 2
Digit sum: 9
Digit product: 20
Digital root: 9
Palindrome: No
Bit width: 6 bits
Reversed: 54
Recamán's sequence: a(30) = 45
Square (n²): 2,025
Cube (n³): 91,125
Divisor count: 6
σ(n) — sum of divisors: 78
φ(n) — Euler's totient: 24
Sum of prime factors: 11

Primality

Prime factorization: 3 ² × 5

Nearest primes: 43 (−2) · 47 (+2)

Divisors & multiples

All divisors (6)

1 · 3 · 5 · 9 · 15 · 45

Aliquot sum (sum of proper divisors): 33

Factor pairs (a × b = 45)

1 × 45

3 × 15

5 × 9

First multiples

45 · 90 (double) · 135 · 180 · 225 · 270 · 315 · 360 · 405 · 450

Sums & aliquot sequence

As a sum of two squares: 3² + 6²

As consecutive integers: 22 + 23 14 + 15 + 16 7 + 8 + 9 + 10 + 11 5 + 6 + 7 + 8 + 9 + 10

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

Continued fraction of √n

√45 = [6; (1, 2, 2, 2, 1, 12)]

Period length 6 — the block in parentheses repeats forever.

Representations

In words: forty-five
Ordinal: 45th
Roman numeral: XLV
Binary: 101101
Octal: 55
Hexadecimal: 0x2D
Base64: LQ==
One's complement: 210 (8-bit)
Scientific notation: 4.5 × 10¹

In other bases

ternary (3) 1200

quaternary (4) 231

quinary (5) 140

senary (6) 113

septenary (7) 63

nonary (9) 50

undecimal (11) 41

duodecimal (12) 39

tridecimal (13) 36

tetradecimal (14) 33

pentadecimal (15) 30

Palindromic in base 2

As an angle

45°

45° ≈ 0.785 rad

Compass bearing: NE (northeast)

Why does a circle have 360 degrees? →

Historical numeral systems

Babylonian (base 60): 𒌋𒌋𒌋𒌋𒁹𒁹𒁹𒁹𒁹
Egyptian hieroglyphic: 𓎆𓎆𓎆𓎆𓏺𓏺𓏺𓏺𓏺
Greek (Milesian): μεʹ
Mayan (base 20): 𝋢·𝋥
Chinese: 四十五
Chinese (financial): 肆拾伍

In other modern scripts

Eastern Arabic ٤٥ Devanagari ४५ Bengali ৪৫ Tamil ௪௫ Thai ๔๕ Tibetan ༤༥ Khmer ៤៥ Lao ໔໕ Burmese ၄၅

Digit at this position in famous constants

π — Pi (π): Digit 45 = 9
e — Euler's number (e): Digit 45 = 9
φ — Golden ratio (φ): Digit 45 = 7
√2 — Pythagoras's (√2): Digit 45 = 7
ln 2 — Natural log of 2: Digit 45 = 3
γ — Euler-Mascheroni (γ): Digit 45 = 3

Also seen as

ASCII character

As an ASCII codepoint, 45 is -. Printable ASCII character -.

Hex color

#00002D

RGB(0, 0, 45)

IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.0.0.45.

Address: 0.0.0.45
Class: reserved
IPv4-mapped IPv6: ::ffff:0.0.0.45

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

US numbered highway

Matches numbered highway designation:

I-45 — Galveston to Dallas, TX.

Interstate 45 on Wikipedia ↗

Geographic coordinate

As a geographic coordinate in degrees, this matches:

45th parallel (latitude) — Halfway between the equator and the pole; crosses through Oregon, Minnesota, Maine, France, Italy, Croatia.

World map (equirectangular projection) — Latitude 45° — 45th parallel

Musical pitch

Heard as a frequency, 45 Hz is closest to:

Concert pitch (A4 = 440 Hz): F♯1 (46.2 Hz, -47¢ — about midway to F1)
Scientific pitch (C4 = 256 Hz): F♯1 (45.3 Hz, -10¢)
Baroque pitch (A4 = 415 Hz): G1 (46.2 Hz, -46¢ — about midway to F♯1)

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

As a MIDI note number, 45 is A2 (110 Hz at concert pitch). (very low — many laptop and phone speakers can't reproduce it)

Atomic number

On the periodic table, atomic number 45 is Rhodium (Rh) — period 5.

Rhodium on Wikipedia ↗

Angle

45° is π/4 radians — half a right angle, the angle of an isosceles right triangle.