46,656
46,656 is the number of possible outcomes when rolling six dice.
Where 46,656 fits
Why 46,656 is special
Six to the sixth power. Probability problems involving several dice grow beyond intuition quickly, which is why gambling odds were misjudged for centuries before the mathematics was worked out.
46,656 is part of
Factors & digit properties
- Divisors (49)
- 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 64, 72, 81, 96, 108, 144, 162, 192, 216, 243, 288, 324, 432, 486, 576, 648, 729, 864, 972, 1296, 1458, 1728, 1944, 2592, 2916, 3888, 5184, 5832, 7776, 11664, 15552, 23328, 46656
- Prime factorisation
- 2^6 × 3^6
- Digit sum
- 27
- Digital root
- 9
Representations
- Decimal
- 46656
- Scientific notation
- 4.666 × 10^4
Roman numerals
Roman numerals as modelled here goes up to 3,999.
Binary
1 0 1 1 0 1 1 0 0 1 0 0 0 0 0 0
1 × 32,768 + 0 × 16,384 + 1 × 8,192 + 1 × 4,096 + 0 × 2,048 + 1 × 1,024 + 1 × 512 + 0 × 256 + 0 × 128 + 1 × 64 + 0 × 32 + 0 × 16 + 0 × 8 + 0 × 4 + 0 × 2 + 0 × 1 = 46,656
Octal
1 3 3 1 0 0
1 × 32,768 + 3 × 4,096 + 3 × 512 + 1 × 64 + 0 × 8 + 0 × 1 = 46,656
Hexadecimal
b 6 4 0
b × 4,096 + 6 × 256 + 4 × 16 + 0 × 1 = 46,656
Read as powers of two: 32,768 + 8,192 + 4,096 + 1,024 + 512 + 64 = 46,656.
In historical numeral systems
Egyptian
4 fingers, 6 lotuses, 6 coils of rope, 5 hobbles, 6 strokes
4 × 10,000 + 6 × 1,000 + 6 × 100 + 5 × 10 + 6 × 1 = 46,656. 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
- Powerful number
- Harshad (Niven) number
Mathematics
Six dice have 46,656 outcomes. The rapid growth is why gamblers systematically misjudged compound odds, and why correspondence about dice problems between Pascal and Fermat founded probability theory.
DocumentedMathematics
Common questions
Is 46,656 a prime number?
No, 46,656 is not prime.
What are the factors of 46,656?
The factors of 46,656 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 64, 72, 81, 96, 108, 144, 162, 192, 216, 243, 288, 324, 432, 486, 576, 648, 729, 864, 972, 1296, 1458, 1728, 1944, 2592, 2916, 3888, 5184, 5832, 7776, 11664, 15552, 23328, 46656.
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