The number 10007
10007 is a twin prime (10007 and 10009 are both prime) and the 1230th prime number. Its only divisors are 1 and 10007.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 10007: a twin prime (10007 and 10009 are both prime); the 1230th prime number.
- 2
10007 is prime, so its only factors are 1 and 10007. It is the 1230th prime; the next prime is 10009 and the one before is 9973.
- 3
The divisors add up to 10008; without 10007 itself that is 1, so 10007 is deficient (1 is less than 10007). Euler's totient φ(10007) = 10006 numbers up to 10007 share no factor with it.
- 4
The digits of 10007 add up to 8, and repeating that until one digit is left gives the digital root 8. The Collatz sequence (halve if even, else 3n+1) takes 179 steps to reach 1.
10007 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 10008 |
| Euler totient φ(n) | 10006 |
| Square | 100140049 |
| Cube | 1002101470343 |
| Square root | 100.034994 |
| Digit sum / digital root | 8 / 8 |
| Collatz steps to 1 | 179 |
| Scientific notation | 1.0007 × |
10007 in other forms
| Form | Value |
|---|---|
| In words | ten thousand and seven |
| Binary (base 2) | 10011100010111 |
| Octal (base 8) | 23427 |
| Hexadecimal (base 16) | 2717 |
| Base 3 | 111201122 |
| As time | 10007 seconds = 2 h 46 min 47 s |
Is 10007 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 4) | 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 8) | 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 8) | 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 10007 a prime number?
Yes. 10007 is divisible only by 1 and itself.
What are the factors of 10007?
1, 10007.
What is 10007 in binary?
10011100010111 (hexadecimal 2717, octal 23427).
What is the square root of 10007?
About 100.0350.
Is 10007 divisible by 3?
No. Its digits add up to 8, which is not a multiple of 3.
What is special about the number 10007?
10007 is a twin prime (10007 and 10009 are both prime); the 1230th prime number.