The number 6007
6007 is the 784th prime number. Its only divisors are 1 and 6007.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 6007: the 784th prime number.
- 2
6007 is prime, so its only factors are 1 and 6007. It is the 784th prime; the next prime is 6011 and the one before is 5987.
- 3
The divisors add up to 6008; without 6007 itself that is 1, so 6007 is deficient (1 is less than 6007). Euler's totient φ(6007) = 6006 numbers up to 6007 share no factor with it.
- 4
The digits of 6007 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 41 steps to reach 1.
6007 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 6008 |
| Euler totient φ(n) | 6006 |
| Square | 36084049 |
| Cube | 216756882343 |
| Square root | 77.504839 |
| Digit sum / digital root | 13 / 4 |
| Collatz steps to 1 | 41 |
| Scientific notation | 6.007 × |
6007 in other forms
| Form | Value |
|---|---|
| In words | six thousand and seven |
| Binary (base 2) | 1011101110111 |
| Octal (base 8) | 13567 |
| Hexadecimal (base 16) | 1777 |
| Base 3 | 22020111 |
| As time | 6007 seconds = 1 h 40 min 7 s |
Is 6007 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 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 4) | 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 1) | 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 6007 a prime number?
Yes. 6007 is divisible only by 1 and itself.
What are the factors of 6007?
1, 6007.
What is 6007 in binary?
1011101110111 (hexadecimal 1777, octal 13567).
What is the square root of 6007?
About 77.5048.
Is 6007 divisible by 3?
No. Its digits add up to 13, which is not a multiple of 3.
What is special about the number 6007?
6007 is the 784th prime number.