The number 59049
59049 is a perfect power () and a perfect square (243²). Its prime factorisation is . Divisors (11): 1, 3, 9, 27, 81, 243, 729, 2187, 6561, 19683, 59049.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 59049: a perfect power (); a perfect square (243²); a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 27.
- 2
59049 is composite. Its prime factorisation is
- 3
The divisors add up to 88573; without 59049 itself that is 29524, so 59049 is deficient (29524 is less than 59049). Euler's totient φ(59049) = 39366 numbers up to 59049 share no factor with it.
- 4
The digits of 59049 add up to 27, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 135 steps to reach 1.
LaTeX source of the formulas on this page
\[ 59049 = 3^{10} \]59049 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 11 |
| Sum of divisors | 88573 |
| Euler totient φ(n) | 39366 |
| Square | 3486784401 |
| Cube | 205891132094649 |
| Square root | 243 |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 135 |
| Scientific notation | 5.9049 × |
| Perfect power |
59049 in other forms
| Form | Value |
|---|---|
| In words | fifty-nine thousand and forty-nine |
| Binary (base 2) | 1110011010101001 |
| Octal (base 8) | 163251 |
| Hexadecimal (base 16) | E6A9 |
| Base 3 | 10000000000 |
| As time | 59049 seconds = 16 h 24 min 9 s |
Is 59049 divisible by 2 to 12?
| 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 (59049 ÷ 3 = 19683) | 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 4) | 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 (59049 ÷ 9 = 6561) | 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 1) | 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. |
Questions
Is 59049 a prime number?
No. 59049 = , so it is divisible by 3.
What are the factors of 59049?
1, 3, 9, 27, 81, 243, 729, 2187, 6561, 19683, 59049.
What is 59049 in binary?
1110011010101001 (hexadecimal E6A9, octal 163251).
What is the square root of 59049?
243, because 243 × 243 = 59049.
Is 59049 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 59049?
59049 is a perfect power (); a perfect square (243²); a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 27.