The number 729

No. 729 = 3^6, so it is divisible by 3.

729 is a perfect power (3^6); a perfect square (27²).

729 is a perfect power ( $3^{6}$ ) and a perfect square (27²). Its prime factorisation is $3^{6}$ . Divisors (7): 1, 3, 9, 27, 81, 243, 729.

Number

Pick any whole number from 1 to 100,000.

729 = 3^{6}

How to work it out

1
What is special about 729: a perfect power ( $3^{6}$ ); a perfect square (27²).
2
729 is composite. Its prime factorisation is
$729 = 3^{6}$
3
The divisors add up to 1093; without 729 itself that is 364, so 729 is deficient (364 is less than 729). Euler's totient φ(729) = 486 numbers up to 729 share no factor with it.
4
The digits of 729 add up to 18, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 33 steps to reach 1.

LaTeX source of the formulas on this page

\[ 729 = 3^{6} \]

Form	Value
In words	seven hundred and twenty-nine
Roman numerals	DCCXXIX
Binary (base 2)	1011011001
Octal (base 8)	1331
Hexadecimal (base 16)	2D9
Base 3	1000000
As time	729 seconds = 12 min 9 s

Divisor	Answer	Rule
2	No (remainder 1)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (729 ÷ 3 = 243)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	No (remainder 1)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	No (remainder 4)	A number is divisible by 5 if the last digit is 0 or 5.
6	No (remainder 3)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	No (remainder 1)	A number is divisible by 7 if double the last digit and subtract it from the rest: the result is a multiple of 7.
8	No (remainder 1)	A number is divisible by 8 if the last three digits make a multiple of 8.
9	Yes (729 ÷ 9 = 81)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	No (remainder 9)	A number is divisible by 10 if the last digit is 0.
11	No (remainder 3)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	No (remainder 9)	A number is divisible by 12 if it is divisible by both 3 and 4.

Is 729 a prime number?

No. 729 = $3^{6}$ , so it is divisible by 3.

What are the factors of 729?

1, 3, 9, 27, 81, 243, 729.

What is 729 in binary?

1011011001 (hexadecimal 2D9, octal 1331).

What is the square root of 729?

27, because 27 × 27 = 729.

What is 729 in Roman numerals?

DCCXXIX.

Is 729 divisible by 3?

Yes. Its digits add up to 18, a multiple of 3.

What is special about the number 729?

729 is a perfect power ( $3^{6}$ ); a perfect square (27²).