81
81 is both a perfect square (9²) and a fourth power (3⁴), and the atomic number of thallium.
Where 81 fits
Why 81 is special
81's dual identity — square and fourth power at once — is a genuine mathematical curiosity most two-digit numbers don't share.
Same number, different meanings
How 81 is understood across different contexts — never implying one meaning because of another.
- Mathematics
81's dual identity — square and fourth power at once — is a genuine mathematical curiosity most two-digit numbers don't share.
- History
Element 81 acquired a reputation no other element has, and the reason is chemistry rather than folklore: thallium sulfate is colourless, tasteless and readily dissolved, and its symptoms — hair loss, nerve pain — resemble ordinary illness. That combination made it both an effective rodenticide and a recurring feature of criminal cases from the 1930s onwards, which is why it was withdrawn as a domestic pesticide in the United States in 1972 and restricted across the European Union. Prussian blue is the standard antidote.
- Geography
+81 reaches Japan, in the 8x block covering East Asia alongside +82 South Korea and +86 China. The regional grouping means a leading 8 on an international number is a reasonable first guess at the continent.
- Science
81 is the atomic number of thallium. Once used in rat poison and once a favoured poison in fiction and fact because it is tasteless and slow-acting, it is now largely confined to specialist electronics.
81 is part of
Factors & digit properties
- Divisors (5)
- 1, 3, 9, 27, 81
- Prime factorisation
- 3^4
- Digit sum
- 9
- Digital root
- 9
Representations
- Decimal
- 81
- Scientific notation
- 8.100 × 10^1
Roman numerals
L X X X I
Binary
1 0 1 0 0 0 1
1 × 64 + 0 × 32 + 1 × 16 + 0 × 8 + 0 × 4 + 0 × 2 + 1 × 1 = 81
Octal
1 2 1
1 × 64 + 2 × 8 + 1 × 1 = 81
Hexadecimal
5 1
5 × 16 + 1 × 1 = 81
Read as powers of two: 64 + 16 + 1 = 81.
In historical numeral systems
Egyptian
8 hobbles, 1 stroke
8 × 10 + 1 × 1 = 81. The signs are simply repeated and added; where they sit on the line is a matter of layout, not value.
Babylonian
1 vertical wedge (sixties place), 2 corner wedges + 1 vertical wedge (units place)
1 × 60 + 21 = 81. Places are separated by a space on the tablet, with the higher place written first.
Greek (Ionic)
pi, then alpha, marked as a numeral
pi-alpha + keraia
pi + alpha written in descending order and added — the letters carry their values wherever they stand, so this is addition, not place value.
Hebrew numerals
pe, then alef
pe-alef
pe (80) + alef (1) = 81, written in descending order.
Chinese numerals
bā shí yī
bā shí yī
八 before 十 multiplies it: 8 tens. 一 after it adds 1. The written form mirrors the arithmetic — "bā shí yī". The financial (anti-fraud) form is 捌拾壹.
Maya
4 dots (upper, twenties place) over 1 dot (lower, units place)
4 × 20 + 1 = 81. 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
- Powerful number
- Harshad (Niven) number
Related numbers & connections
81 is the square of 9 (9² = 81).
View 9 →Japan's ISO numeric code and calling code. Both appear on the same customs and payment documents, serving different systems within them.
View 392 →History
Element 81 acquired a reputation no other element has, and the reason is chemistry rather than folklore: thallium sulfate is colourless, tasteless and readily dissolved, and its symptoms — hair loss, nerve pain — resemble ordinary illness. That combination made it both an effective rodenticide and a recurring feature of criminal cases from the 1930s onwards, which is why it was withdrawn as a domestic pesticide in the United States in 1972 and restricted across the European Union. Prussian blue is the standard antidote.
DocumentedHistoryGeography: United States and the European UnionPeriod: 1930s – 1970s
Geography
+81 reaches Japan, in the 8x block covering East Asia alongside +82 South Korea and +86 China. The regional grouping means a leading 8 on an international number is a reasonable first guess at the continent.
DocumentedGeographyGeography: Japan
Science
81 is the atomic number of thallium. Once used in rat poison and once a favoured poison in fiction and fact because it is tasteless and slow-acting, it is now largely confined to specialist electronics.
DocumentedScience
Mathematics
81 = 9² = 3⁴ — both a perfect square and a fourth power.
DocumentedMathematics
Common questions
Why is 81 both a square and a fourth power?
Because 81 = 3⁴, and a fourth power is a square squared: 3⁴ = (3²)² = 9². Every fourth power is automatically a square for the same reason, so 16, 81, 256 and 625 all qualify. 81 is the smallest one above 16.
Is 81 a prime number?
No, 81 is not prime.
What are the factors of 81?
The factors of 81 are 1, 3, 9, 27, 81.
What is 81 in Roman numerals?
81 in Roman numerals is LXXXI.
About this page's data
Mathematical facts:computed directly from the number's value — nothing to source or verify externally.
Contextual records: 4 reviewer-confirmed records, sourced and reviewed before publication.
Last reviewed: 15 July 2026