The number 1039
1039 is the 175th prime number. Its only divisors are 1 and 1039.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 1039: the 175th prime number; a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
1039 is prime, so its only factors are 1 and 1039. It is the 175th prime; the next prime is 1049 and the one before is 1033.
- 3
The divisors add up to 1040; without 1039 itself that is 1, so 1039 is deficient (1 is less than 1039). Euler's totient φ(1039) = 1038 numbers up to 1039 share no factor with it.
- 4
The digits of 1039 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 62 steps to reach 1.
1039 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 1040 |
| Euler totient φ(n) | 1038 |
| Square | 1079521 |
| Cube | 1121622319 |
| Square root | 32.233523 |
| Digit sum / digital root | 13 / 4 |
| Collatz steps to 1 | 62 |
| Scientific notation | 1.039 × |
1039 in other forms
| Form | Value |
|---|---|
| In words | one thousand and thirty-nine |
| Roman numerals | MXXXIX |
| Binary (base 2) | 10000001111 |
| Octal (base 8) | 2017 |
| Hexadecimal (base 16) | 40F |
| Base 3 | 1102111 |
| As time | 1039 seconds = 17 min 19 s |
Is 1039 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 3) | 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 5) | 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 1039 a prime number?
Yes. 1039 is divisible only by 1 and itself.
What are the factors of 1039?
1, 1039.
What is 1039 in binary?
10000001111 (hexadecimal 40F, octal 2017).
What is the square root of 1039?
About 32.2335.
What is 1039 in Roman numerals?
MXXXIX.
Is 1039 divisible by 3?
No. Its digits add up to 13, which is not a multiple of 3.
What is special about the number 1039?
1039 is the 175th prime number; a happy number: repeatedly adding the squares of its digits reaches 1.