The number 13903
13903 is a twin prime (13901 and 13903 are both prime) and the 1643rd prime number. Its only divisors are 1 and 13903.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 13903: a twin prime (13901 and 13903 are both prime); the 1643rd prime number; a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
13903 is prime, so its only factors are 1 and 13903. It is the 1643rd prime; the next prime is 13907 and the one before is 13901.
- 3
The divisors add up to 13904; without 13903 itself that is 1, so 13903 is deficient (1 is less than 13903). Euler's totient φ(13903) = 13902 numbers up to 13903 share no factor with it.
- 4
The digits of 13903 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 112 steps to reach 1.
13903 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 13904 |
| Euler totient φ(n) | 13902 |
| Square | 193293409 |
| Cube | 2687358265327 |
| Square root | 117.910983 |
| Digit sum / digital root | 16 / 7 |
| Collatz steps to 1 | 112 |
| Scientific notation | 1.3903 × |
13903 in other forms
| Form | Value |
|---|---|
| In words | thirteen thousand nine hundred and three |
| Binary (base 2) | 11011001001111 |
| Octal (base 8) | 33117 |
| Hexadecimal (base 16) | 364F |
| Base 3 | 201001221 |
| As time | 13903 seconds = 3 h 51 min 43 s |
Is 13903 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 3) | 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 7) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 3) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 10) | 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 13903 a prime number?
Yes. 13903 is divisible only by 1 and itself.
What are the factors of 13903?
1, 13903.
What is 13903 in binary?
11011001001111 (hexadecimal 364F, octal 33117).
What is the square root of 13903?
About 117.9110.
Is 13903 divisible by 3?
No. Its digits add up to 16, which is not a multiple of 3.
What is special about the number 13903?
13903 is a twin prime (13901 and 13903 are both prime); the 1643rd prime number; a happy number: repeatedly adding the squares of its digits reaches 1.