The number 13009
13009 is a twin prime (13007 and 13009 are both prime) and the 1551st prime number. Its only divisors are 1 and 13009.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 13009: a twin prime (13007 and 13009 are both prime); the 1551st prime number; a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
13009 is prime, so its only factors are 1 and 13009. It is the 1551st prime; the next prime is 13033 and the one before is 13007.
- 3
The divisors add up to 13010; without 13009 itself that is 1, so 13009 is deficient (1 is less than 13009). Euler's totient φ(13009) = 13008 numbers up to 13009 share no factor with it.
- 4
The digits of 13009 add up to 13, and repeating that until one digit is left gives the digital root 4. The Collatz sequence (halve if even, else 3n+1) takes 138 steps to reach 1.
13009 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 13010 |
| Euler totient φ(n) | 13008 |
| Square | 169234081 |
| Cube | 2201566159729 |
| Square root | 114.057003 |
| Digit sum / digital root | 13 / 4 |
| Collatz steps to 1 | 138 |
| Scientific notation | 1.3009 × |
13009 in other forms
| Form | Value |
|---|---|
| In words | thirteen thousand and nine |
| Binary (base 2) | 11001011010001 |
| Octal (base 8) | 31321 |
| Hexadecimal (base 16) | 32D1 |
| Base 3 | 122211211 |
| As time | 13009 seconds = 3 h 36 min 49 s |
Is 13009 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 | No (remainder 1) | 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 1) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 3) | 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 | No (remainder 4) | 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 7) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 1) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 13009 a prime number?
Yes. 13009 is divisible only by 1 and itself.
What are the factors of 13009?
1, 13009.
What is 13009 in binary?
11001011010001 (hexadecimal 32D1, octal 31321).
What is the square root of 13009?
About 114.0570.
Is 13009 divisible by 3?
No. Its digits add up to 13, which is not a multiple of 3.
What is special about the number 13009?
13009 is a twin prime (13007 and 13009 are both prime); the 1551st prime number; a happy number: repeatedly adding the squares of its digits reaches 1.