1728
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Number
$1728$ (one thousand, seven hundred and twenty-eight) is:
- $2^6 \times 3^3$
- The $3$rd power of $12$ after $(1)$, $12$, $144$:
- $1728 = 12^3$
- The $12$th cube number after $1$, $8$, $27$, $64$, $125$, $216$, $343$, $512$, $729$, $1000$, $1331$:
- $1728 = 12 \times 12 \times 12 = \paren {2^2 \times 3}^3$
- Hence in duodecimal notation:
- $1000$
- The $363$rd harshad number:
- $1728 = 96 \times 18 = 96 \times \paren {1 + 7 + 2 + 8}$
Also see
- Previous ... Next: Sequence of Powers of 12
- Previous ... Next: Cubes which are Sum of Three Cubes
- Previous ... Next: Cube Number
- Previous ... Next: Harshad Number
Historical Note
There are $12^3 = 1728$ cubic inches in $1$ cubic foot.
Sources
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $1728$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $1728$