The number 13007
13007 is a twin prime (13007 and 13009 are both prime) and the 1550th prime number. Its only divisors are 1 and 13007.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 13007: a twin prime (13007 and 13009 are both prime); the 1550th prime number.
- 2
13007 is prime, so its only factors are 1 and 13007. It is the 1550th prime; the next prime is 13009 and the one before is 13003.
- 3
The divisors add up to 13008; without 13007 itself that is 1, so 13007 is deficient (1 is less than 13007). Euler's totient φ(13007) = 13006 numbers up to 13007 share no factor with it.
- 4
The digits of 13007 add up to 11, and repeating that until one digit is left gives the digital root 2. The Collatz sequence (halve if even, else 3n+1) takes 63 steps to reach 1.
13007 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 13008 |
| Euler totient φ(n) | 13006 |
| Square | 169182049 |
| Cube | 2200550911343 |
| Square root | 114.048235 |
| Digit sum / digital root | 11 / 2 |
| Collatz steps to 1 | 63 |
| Scientific notation | 1.3007 × |
13007 in other forms
| Form | Value |
|---|---|
| In words | thirteen thousand and seven |
| Binary (base 2) | 11001011001111 |
| Octal (base 8) | 31317 |
| Hexadecimal (base 16) | 32CF |
| Base 3 | 122211202 |
| As time | 13007 seconds = 3 h 36 min 47 s |
Is 13007 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 2) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 3) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 2) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 5) | 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 7) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 2) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 7) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 5) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 11) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 13007 a prime number?
Yes. 13007 is divisible only by 1 and itself.
What are the factors of 13007?
1, 13007.
What is 13007 in binary?
11001011001111 (hexadecimal 32CF, octal 31317).
What is the square root of 13007?
About 114.0482.
Is 13007 divisible by 3?
No. Its digits add up to 11, which is not a multiple of 3.
What is special about the number 13007?
13007 is a twin prime (13007 and 13009 are both prime); the 1550th prime number.