45
45 is a triangular number, the atomic number of rhodium, and the standard playback speed (45 RPM) for vinyl singles.
- Odd
- Composite
Where 45 fits
Why 45 is special
45's mathematical identity (triangular, the sum of 1 through 9) sits alongside a real audio-engineering standard still referenced whenever vinyl singles are discussed.
Same number, different meanings
How 45 is understood across different contexts — never implying one meaning because of another.
- Mathematics
45's mathematical identity (triangular, the sum of 1 through 9) sits alongside a real audio-engineering standard still referenced whenever vinyl singles are discussed.
- Media & popular culture
The seven-inch 45 rpm disc was the standard single format for four decades. Its wide centre hole exists so that jukebox mechanisms could handle it, which is why domestic players needed an adapter.
- Sport
Football has been played in two 45-minute halves since 1877. Almost every other rule has been revised repeatedly; the duration has not.
- Science
45 is the atomic number of rhodium. It is one of the rarest and typically the most expensive of the precious metals, used chiefly in catalytic converters, where it strips nitrogen oxides from exhaust gases.
45 is part of
Factors & digit properties
- Divisors (6)
- 1, 3, 5, 9, 15, 45
- Prime factorisation
- 3^2 × 5
- Digit sum
- 9
- Digital root
- 9
Representations
- Decimal
- 45
- Scientific notation
- 4.500 × 10^1
Roman numerals
X L V
XLV uses the subtractive pair XL: ten before fifty — fifty minus ten.
Binary
1 0 1 1 0 1
1 × 32 + 0 × 16 + 1 × 8 + 1 × 4 + 0 × 2 + 1 × 1 = 45
Octal
5 5
5 × 8 + 5 × 1 = 45
Hexadecimal
2 d
2 × 16 + d × 1 = 45
Read as powers of two: 32 + 8 + 4 + 1 = 45.
In historical numeral systems
Egyptian
4 hobbles, 5 strokes
4 × 10 + 5 × 1 = 45. The signs are simply repeated and added; where they sit on the line is a matter of layout, not value.
Babylonian
4 corner wedges + 5 vertical wedges
45 fits in a single sexagesimal place: 4 corner wedges + 5 vertical wedges.
Greek (Ionic)
mu, then epsilon, marked as a numeral
mu-epsilon + keraia
mu + epsilon written in descending order and added — the letters carry their values wherever they stand, so this is addition, not place value.
Hebrew numerals
mem, then he
mem-he
mem (40) + he (5) = 45, written in descending order.
Chinese numerals
sì shí wǔ
sì shí wǔ
四 before 十 multiplies it: 4 tens. 五 after it adds 5. The written form mirrors the arithmetic — "sì shí wǔ". The financial (anti-fraud) form is 肆拾伍.
Maya
2 dots (upper, twenties place) over 1 bar (lower, units place)
2 × 20 + 5 = 45. Places stack vertically with the smallest at the bottom, so the upper group is worth twenty times the lower.
Systems that simply cannot reach this value are left out. Where a script needs a font most readers do not have, the reading is given instead of the glyphs — see number systems for each system in full.
Other mathematical patterns
- Triangular number
- Deficient number
- Kaprekar number
- Hexagonal number
- Harshad (Niven) number
Related numbers & connections
9 is a factor of 45 (9 × 5 = 45).
View 9 →The seven-inch single turns at forty-five revolutions per minute and was the standard single format for four decades.
Media & popular culture
The seven-inch 45 rpm disc was the standard single format for four decades. Its wide centre hole exists so that jukebox mechanisms could handle it, which is why domestic players needed an adapter.
DocumentedMedia & popular cultureGeography: United States, adopted internationallyPeriod: 1949–The 45 rpm seven-inch disc was introduced by RCA Victor in 1949 in direct competition with Columbia's 33⅓ format. The market settled on both: albums at 33⅓ and singles at 45.
DocumentedMedia & popular cultureGeography: United States, adopted internationallyPeriod: 1949–45 RPM is the standard playback speed for 7-inch vinyl singles, distinct from the slower 33⅓ RPM used for full-length LP albums.
DocumentedMedia & popular culture
Sport
Football has been played in two 45-minute halves since 1877. Almost every other rule has been revised repeatedly; the duration has not.
DocumentedSportGeography: Association football worldwidePeriod: from 1877
Mathematics
45 degrees is half a right angle and the angle of a square's diagonal. A right-angled triangle with two 45-degree angles is isosceles, and its hypotenuse is always the side length times the square root of 2 — a relationship used constantly in construction and drawing.
DocumentedMathematics
Science
45 is the atomic number of rhodium. It is one of the rarest and typically the most expensive of the precious metals, used chiefly in catalytic converters, where it strips nitrogen oxides from exhaust gases.
DocumentedScience
Common questions
Why is a football half 45 minutes?
It was fixed in 1877 when the two English rule-making bodies merged their laws, and it has never been revisited. Almost everything else about the game has changed. The clock does not stop, so stoppages are added at the end of each half rather than paused for.
What is the difference between a 45 and a 33?
Playback speed and purpose. A 45 rpm seven-inch disc holds one song a side and was the single format; a 33⅓ rpm twelve-inch holds about twenty minutes a side and was the album. RCA and Columbia introduced them a year apart as rival formats in 1948 and 1949, and the market kept both.
Is 45 a prime number?
No, 45 is not prime.
What are the factors of 45?
The factors of 45 are 1, 3, 5, 9, 15, 45.
What is 45 in Roman numerals?
45 in Roman numerals is XLV. XL is subtractive: ten before fifty — fifty minus ten. Written additively it would be XXXXV, which Roman inscriptions used freely — the strict subtractive form is a later convention.
About this page's data
Mathematical facts:computed directly from the number's value — nothing to source or verify externally.
Contextual records: 6 reviewer-confirmed records, sourced and reviewed before publication.
Last reviewed: 15 July 2026