The number 9009
9009 is a palindrome: it reads 9009 backwards too and a binary palindrome (10001100110001). Its prime factorisation is × 7 × 11 × 13. Divisors (24): 1, 3, 7, 9, 11, 13, 21, 33, 39, 63, 77, 91, 99, 117, 143, 231 … 9009.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 9009: a palindrome: it reads 9009 backwards too; a binary palindrome (10001100110001).
- 2
9009 is composite. Its prime factorisation is
- 3
The divisors add up to 17472; without 9009 itself that is 8463, so 9009 is deficient (8463 is less than 9009). Euler's totient φ(9009) = 4320 numbers up to 9009 share no factor with it.
- 4
The digits of 9009 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 39 steps to reach 1.
LaTeX source of the formulas on this page
\[ 9009 = 3^{2} \times 7 \times 11 \times 13 \]9009 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 17472 |
| Euler totient φ(n) | 4320 |
| Square | 81162081 |
| Cube | 731189187729 |
| Square root | 94.915752 (= 3√1001) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 39 |
| Scientific notation | 9.009 × |
9009 in other forms
| Form | Value |
|---|---|
| In words | nine thousand and nine |
| Binary (base 2) | 10001100110001 |
| Octal (base 8) | 21461 |
| Hexadecimal (base 16) | 2331 |
| Base 3 | 110100200 |
| As time | 9009 seconds = 2 h 30 min 9 s |
Is 9009 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 (9009 ÷ 3 = 3003) | 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 | Yes (9009 ÷ 7 = 1287) | 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 (9009 ÷ 9 = 1001) | 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 | Yes (9009 ÷ 11 = 819) | 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 9009 a prime number?
No. 9009 = × 7 × 11 × 13, so it is divisible by 3.
What are the factors of 9009?
1, 3, 7, 9, 11, 13, 21, 33, 39, 63, 77, 91, 99, 117, 143, 231, 273, 429, 693, 819, 1001, 1287, 3003, 9009.
What is 9009 in binary?
10001100110001 (hexadecimal 2331, octal 21461).
What is the square root of 9009?
About 94.9158, exactly 3√1001.
Is 9009 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 9009?
9009 is a palindrome: it reads 9009 backwards too; a binary palindrome (10001100110001).