40,585
40,585 equals the sum of the factorials of its own digits.
- Odd
- Composite
Where 40,585 fits
Why 40,585 is special
4! + 0! + 5! + 8! + 5! = 40,585. It is the largest of only four such numbers in base ten — 1, 2, 145 and this — and the list is proven complete because beyond seven digits the factorials cannot keep pace.
40,585 is part of
Factors & digit properties
- Divisors (4)
- 1, 5, 8117, 40585
- Prime factorisation
- 5 × 8117
- Digit sum
- 22
- Digital root
- 4
Representations
- Decimal
- 40585
- Scientific notation
- 4.059 × 10^4
Roman numerals
Roman numerals as modelled here goes up to 3,999.
Binary
1 0 0 1 1 1 1 0 1 0 0 0 1 0 0 1
1 × 32,768 + 0 × 16,384 + 0 × 8,192 + 1 × 4,096 + 1 × 2,048 + 1 × 1,024 + 1 × 512 + 0 × 256 + 1 × 128 + 0 × 64 + 0 × 32 + 0 × 16 + 1 × 8 + 0 × 4 + 0 × 2 + 1 × 1 = 40,585
Octal
1 1 7 2 1 1
1 × 32,768 + 1 × 4,096 + 7 × 512 + 2 × 64 + 1 × 8 + 1 × 1 = 40,585
Hexadecimal
9 e 8 9
9 × 4,096 + e × 256 + 8 × 16 + 9 × 1 = 40,585
Read as powers of two: 32,768 + 4,096 + 2,048 + 1,024 + 512 + 128 + 8 + 1 = 40,585.
In historical numeral systems
Egyptian
4 fingers, 5 coils of rope, 8 hobbles, 5 strokes
4 × 10,000 + 5 × 100 + 8 × 10 + 5 × 1 = 40,585. The signs are simply repeated and added; where they sit on the line is a matter of layout, not value.
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
- Happy 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 145 →Mathematically related
- is a multiple of145
why?
Strength 0.50, confidence "high".
Mathematics
4! + 0! + 5! + 8! + 5! = 40,585, the biggest of the four base-ten numbers equal to the sum of their digits' factorials. The set — 1, 2, 145, 40,585 — is proven complete, because past seven digits the factorials cannot grow fast enough to catch up.
DocumentedMathematics
Common questions
Is 40,585 a prime number?
No, 40,585 is not prime.
What are the factors of 40,585?
The factors of 40,585 are 1, 5, 8117, 40585.
About this page's data
Mathematical facts:computed directly from the number's value — nothing to source or verify externally.
Contextual records: 1 reviewer-confirmed record, sourced and reviewed before publication.
Last reviewed: 15 July 2026