40,320
40,320 is 8 factorial — the number of ways to arrange eight distinct objects.
- Even
- Composite
Where 40,320 fits
Why 40,320 is special
40,320 is where factorial growth becomes hard to picture. Eight objects have forty thousand orderings; nine have over three hundred thousand. It is the number of possible orders for a chess rank's eight pieces if all were distinct, and the reason exhaustive search stops being viable so quickly as problems grow.
Factors & digit properties
- Divisors (96)
- 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 28, 30, 32, 35, 36, 40, 42, 45, 48, 56, 60, 63, 64, 70, 72, 80, 84, 90, 96, 105, 112, 120, 126, 128, 140, 144, 160, 168, 180, 192, 210, 224, 240, 252, 280, 288, 315, 320, 336, 360, 384, 420, 448, 480, 504, 560, 576, 630, 640, 672, 720, 840, 896, 960, 1008, 1120, 1152, 1260, 1344, 1440, 1680, 1920, 2016, 2240, 2520, 2688, 2880, 3360, 4032, 4480, 5040, 5760, 6720, 8064, 10080, 13440, 20160, 40320
- Prime factorisation
- 2^7 × 3^2 × 5 × 7
- Digit sum
- 9
- Digital root
- 9
Representations
- Decimal
- 40320
- Scientific notation
- 4.032 × 10^4
Roman numerals
Roman numerals as modelled here goes up to 3,999.
Binary
1 0 0 1 1 1 0 1 1 0 0 0 0 0 0 0
1 × 32,768 + 0 × 16,384 + 0 × 8,192 + 1 × 4,096 + 1 × 2,048 + 1 × 1,024 + 0 × 512 + 1 × 256 + 1 × 128 + 0 × 64 + 0 × 32 + 0 × 16 + 0 × 8 + 0 × 4 + 0 × 2 + 0 × 1 = 40,320
Octal
1 1 6 6 0 0
1 × 32,768 + 1 × 4,096 + 6 × 512 + 6 × 64 + 0 × 8 + 0 × 1 = 40,320
Hexadecimal
9 d 8 0
9 × 4,096 + d × 256 + 8 × 16 + 0 × 1 = 40,320
Read as powers of two: 32,768 + 4,096 + 2,048 + 1,024 + 256 + 128 = 40,320.
In historical numeral systems
Egyptian
4 fingers, 3 coils of rope, 2 hobbles
4 × 10,000 + 3 × 100 + 2 × 10 = 40,320. 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
- Abundant number
- Factorial number
- Harshad (Niven) number
Related numbers & connections
362,880 is 9!, nine times 8!. It is also the number of ways to fill one row of a Sudoku grid with the digits 1 to 9.
View 362880 →Mathematics
Eight items have 40,320 orderings, nine have 362,880, and ten have over three and a half million. That growth is why brute-forcing arrangements is viable for tiny inputs and hopeless immediately after — the practical reason so much of computer science is about avoiding enumeration.
DocumentedMathematics
Common questions
Is 40,320 a prime number?
No, 40,320 is not prime.
What are the factors of 40,320?
The factors of 40,320 are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 28, 30, 32, 35, 36, 40, 42, 45, 48, 56, 60, 63, 64, 70, 72, 80, 84, 90, 96, 105, 112, 120, 126, 128, 140, 144, 160, 168, 180, 192, 210, 224, 240, 252, 280, 288, 315, 320, 336, 360, 384, 420, 448, 480, 504, 560, 576, 630, 640, 672, 720, 840, 896, 960, 1008, 1120, 1152, 1260, 1344, 1440, 1680, 1920, 2016, 2240, 2520, 2688, 2880, 3360, 4032, 4480, 5040, 5760, 6720, 8064, 10080, 13440, 20160, 40320.
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