The number 13997
13997 is a twin prime (13997 and 13999 are both prime) and the 1651st prime number. Its only divisors are 1 and 13997.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 13997: a twin prime (13997 and 13999 are both prime); the 1651st prime number.
- 2
13997 is prime, so its only factors are 1 and 13997. It is the 1651st prime; the next prime is 13999 and the one before is 13967.
- 3
The divisors add up to 13998; without 13997 itself that is 1, so 13997 is deficient (1 is less than 13997). Euler's totient φ(13997) = 13996 numbers up to 13997 share no factor with it.
- 4
The digits of 13997 add up to 29, and repeating that until one digit is left gives the digital root 2. The Collatz sequence (halve if even, else 3n+1) takes 133 steps to reach 1.
13997 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 13998 |
| Euler totient φ(n) | 13996 |
| Square | 195916009 |
| Cube | 2742236377973 |
| Square root | 118.308918 |
| Digit sum / digital root | 29 / 2 |
| Collatz steps to 1 | 133 |
| Scientific notation | 1.3997 × |
13997 in other forms
| Form | Value |
|---|---|
| In words | thirteen thousand nine hundred and ninety-seven |
| Binary (base 2) | 11011010101101 |
| Octal (base 8) | 33255 |
| Hexadecimal (base 16) | 36AD |
| Base 3 | 201012102 |
| As time | 13997 seconds = 3 h 53 min 17 s |
Is 13997 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 1) | 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 5) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 2) | 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 5) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 5) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 13997 a prime number?
Yes. 13997 is divisible only by 1 and itself.
What are the factors of 13997?
1, 13997.
What is 13997 in binary?
11011010101101 (hexadecimal 36AD, octal 33255).
What is the square root of 13997?
About 118.3089.
Is 13997 divisible by 3?
No. Its digits add up to 29, which is not a multiple of 3.
What is special about the number 13997?
13997 is a twin prime (13997 and 13999 are both prime); the 1651st prime number.