145
145 equals the sum of the factorials of its own digits.
- Odd
- Composite
Where 145 fits
Why 145 is special
1! + 4! + 5! = 1 + 24 + 120 = 145. Only four numbers in base ten do this: 1, 2, 145 and 40,585. The list is complete and proven, not merely unfinished — beyond seven digits the factorials cannot keep up with the number itself.
Factors & digit properties
- Divisors (4)
- 1, 5, 29, 145
- Prime factorisation
- 5 × 29
- Digit sum
- 10
- Digital root
- 1
Representations
- Decimal
- 145
- Scientific notation
- 1.450 × 10^2
Roman numerals
C X L V
CXLV uses the subtractive pair XL: ten before fifty — fifty minus ten.
Binary
1 0 0 1 0 0 0 1
1 × 128 + 0 × 64 + 0 × 32 + 1 × 16 + 0 × 8 + 0 × 4 + 0 × 2 + 1 × 1 = 145
Octal
2 2 1
2 × 64 + 2 × 8 + 1 × 1 = 145
Hexadecimal
9 1
9 × 16 + 1 × 1 = 145
Read as powers of two: 128 + 16 + 1 = 145.
In historical numeral systems
Egyptian
1 coil of rope, 4 hobbles, 5 strokes
1 × 100 + 4 × 10 + 5 × 1 = 145. The signs are simply repeated and added; where they sit on the line is a matter of layout, not value.
Babylonian
2 vertical wedges (sixties place), 2 corner wedges + 5 vertical wedges (units place)
2 × 60 + 25 = 145. Places are separated by a space on the tablet, with the higher place written first.
Greek (Ionic)
rho, then mu, then epsilon, marked as a numeral
rho-mu-epsilon + keraia
rho + 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
qof, then mem, then he
qof-mem-he
qof (100) + mem (40) + he (5) = 145, written in descending order.
Maya
1 bar + 2 dots (upper, twenties place) over 1 bar (lower, units place)
7 × 20 + 5 = 145. 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
- Deficient number
- Pentagonal number
- Semiprime
Related numbers & connections
Both equal the sum of the factorials of their own digits. With 1 and 2 they are the complete set in base ten, and the completeness is proven rather than merely unextended.
View 40585 →The engine and the regional jet it powers defined the fifty-seat category together.
View 3007 →Technology & computing
The Embraer ERJ 145 established the 50-seat regional jet market from 1996, replacing turboprops on thin routes before fuel prices made that size uneconomic.
DocumentedTechnology & computingGeography: Brazil, operated worldwidePeriod: 1996–
Mathematics
1! + 4! + 5! = 145. Only 1, 2, 145 and 40,585 equal the sum of their own digits' factorials in base ten, and the list is proven complete rather than merely unextended — past seven digits the factorials cannot keep pace with the number.
DocumentedMathematics
Common questions
Is 145 a prime number?
No, 145 is not prime.
What are the factors of 145?
The factors of 145 are 1, 5, 29, 145.
What is 145 in Roman numerals?
145 in Roman numerals is CXLV. XL is subtractive: ten before fifty — fifty minus ten. Written additively it would be CXXXXV, 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: 2 reviewer-confirmed records, sourced and reviewed before publication.
Last reviewed: 15 July 2026