The number 10039
10039 is a twin prime (10037 and 10039 are both prime) and the 1233rd prime number. Its only divisors are 1 and 10039.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 10039: a twin prime (10037 and 10039 are both prime); the 1233rd prime number; a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
10039 is prime, so its only factors are 1 and 10039. It is the 1233rd prime; the next prime is 10061 and the one before is 10037.
- 3
The divisors add up to 10040; without 10039 itself that is 1, so 10039 is deficient (1 is less than 10039). Euler's totient φ(10039) = 10038 numbers up to 10039 share no factor with it.
- 4
The digits of 10039 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 65 steps to reach 1.
10039 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 10040 |
| Euler totient φ(n) | 10038 |
| Square | 100781521 |
| Cube | 1011745689319 |
| Square root | 100.194810 |
| Digit sum / digital root | 13 / 4 |
| Collatz steps to 1 | 65 |
| Scientific notation | 1.0039 × |
10039 in other forms
| Form | Value |
|---|---|
| In words | ten thousand and thirty-nine |
| Binary (base 2) | 10011100110111 |
| Octal (base 8) | 23467 |
| Hexadecimal (base 16) | 2737 |
| Base 3 | 111202211 |
| As time | 10039 seconds = 2 h 47 min 19 s |
Is 10039 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 4) | 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 9) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 7) | 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 10039 a prime number?
Yes. 10039 is divisible only by 1 and itself.
What are the factors of 10039?
1, 10039.
What is 10039 in binary?
10011100110111 (hexadecimal 2737, octal 23467).
What is the square root of 10039?
About 100.1948.
Is 10039 divisible by 3?
No. Its digits add up to 13, which is not a multiple of 3.
What is special about the number 10039?
10039 is a twin prime (10037 and 10039 are both prime); the 1233rd prime number; a happy number: repeatedly adding the squares of its digits reaches 1.