The number 9007
9007 is the 1119th prime number. Its only divisors are 1 and 9007.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 9007: the 1119th prime number; a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
9007 is prime, so its only factors are 1 and 9007. It is the 1119th prime; the next prime is 9011 and the one before is 9001.
- 3
The divisors add up to 9008; without 9007 itself that is 1, so 9007 is deficient (1 is less than 9007). Euler's totient φ(9007) = 9006 numbers up to 9007 share no factor with it.
- 4
The digits of 9007 add up to 16, and repeating that until one digit is left gives the digital root 7. The Collatz sequence (halve if even, else 3n+1) takes 78 steps to reach 1.
9007 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 9008 |
| Euler totient φ(n) | 9006 |
| Square | 81126049 |
| Cube | 730702323343 |
| Square root | 94.905216 |
| Digit sum / digital root | 16 / 7 |
| Collatz steps to 1 | 78 |
| Scientific notation | 9.007 × |
9007 in other forms
| Form | Value |
|---|---|
| In words | nine thousand and seven |
| Binary (base 2) | 10001100101111 |
| Octal (base 8) | 21457 |
| Hexadecimal (base 16) | 232F |
| Base 3 | 110100121 |
| As time | 9007 seconds = 2 h 30 min 7 s |
Is 9007 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 5) | 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 7) | 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 9) | 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 9007 a prime number?
Yes. 9007 is divisible only by 1 and itself.
What are the factors of 9007?
1, 9007.
What is 9007 in binary?
10001100101111 (hexadecimal 232F, octal 21457).
What is the square root of 9007?
About 94.9052.
Is 9007 divisible by 3?
No. Its digits add up to 16, which is not a multiple of 3.
What is special about the number 9007?
9007 is the 1119th prime number; a happy number: repeatedly adding the squares of its digits reaches 1.