The number 13999
13999 is a twin prime (13997 and 13999 are both prime) and the 1652nd prime number. Its only divisors are 1 and 13999.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 13999: a twin prime (13997 and 13999 are both prime); the 1652nd prime number.
- 2
13999 is prime, so its only factors are 1 and 13999. It is the 1652nd prime; the next prime is 14009 and the one before is 13997.
- 3
The divisors add up to 14000; without 13999 itself that is 1, so 13999 is deficient (1 is less than 13999). Euler's totient φ(13999) = 13998 numbers up to 13999 share no factor with it.
- 4
The digits of 13999 add up to 31, and repeating that until one digit is left gives the digital root 4. The Collatz sequence (halve if even, else 3n+1) takes 89 steps to reach 1.
13999 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 14000 |
| Euler totient φ(n) | 13998 |
| Square | 195972001 |
| Cube | 2743412041999 |
| Square root | 118.317370 |
| Digit sum / digital root | 31 / 4 |
| Collatz steps to 1 | 89 |
| Scientific notation | 1.3999 × |
13999 in other forms
| Form | Value |
|---|---|
| In words | thirteen thousand nine hundred and ninety-nine |
| Binary (base 2) | 11011010101111 |
| Octal (base 8) | 33257 |
| Hexadecimal (base 16) | 36AF |
| Base 3 | 201012111 |
| As time | 13999 seconds = 3 h 53 min 19 s |
Is 13999 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 6) | 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 13999 a prime number?
Yes. 13999 is divisible only by 1 and itself.
What are the factors of 13999?
1, 13999.
What is 13999 in binary?
11011010101111 (hexadecimal 36AF, octal 33257).
What is the square root of 13999?
About 118.3174.
Is 13999 divisible by 3?
No. Its digits add up to 31, which is not a multiple of 3.
What is special about the number 13999?
13999 is a twin prime (13997 and 13999 are both prime); the 1652nd prime number.