The number 12007
12007 is the 1439th prime number. Its only divisors are 1 and 12007.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 12007: the 1439th prime number.
- 2
12007 is prime, so its only factors are 1 and 12007. It is the 1439th prime; the next prime is 12011 and the one before is 11987.
- 3
The divisors add up to 12008; without 12007 itself that is 1, so 12007 is deficient (1 is less than 12007). Euler's totient φ(12007) = 12006 numbers up to 12007 share no factor with it.
- 4
The digits of 12007 add up to 10, and repeating that until one digit is left gives the digital root 1. The Collatz sequence (halve if even, else 3n+1) takes 68 steps to reach 1.
12007 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 12008 |
| Euler totient φ(n) | 12006 |
| Square | 144168049 |
| Cube | 1731025764343 |
| Square root | 109.576457 |
| Digit sum / digital root | 10 / 1 |
| Collatz steps to 1 | 68 |
| Scientific notation | 1.2007 × |
12007 in other forms
| Form | Value |
|---|---|
| In words | twelve thousand and seven |
| Binary (base 2) | 10111011100111 |
| Octal (base 8) | 27347 |
| Hexadecimal (base 16) | 2EE7 |
| Base 3 | 121110201 |
| As time | 12007 seconds = 3 h 20 min 7 s |
Is 12007 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 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 1) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 2) | 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 1) | 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 6) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 7) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 12007 a prime number?
Yes. 12007 is divisible only by 1 and itself.
What are the factors of 12007?
1, 12007.
What is 12007 in binary?
10111011100111 (hexadecimal 2EE7, octal 27347).
What is the square root of 12007?
About 109.5765.
Is 12007 divisible by 3?
No. Its digits add up to 10, which is not a multiple of 3.
What is special about the number 12007?
12007 is the 1439th prime number.