The number 13967
13967 is the 1650th prime number. Its only divisors are 1 and 13967.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 13967: the 1650th prime number; a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
13967 is prime, so its only factors are 1 and 13967. It is the 1650th prime; the next prime is 13997 and the one before is 13963.
- 3
The divisors add up to 13968; without 13967 itself that is 1, so 13967 is deficient (1 is less than 13967). Euler's totient φ(13967) = 13966 numbers up to 13967 share no factor with it.
- 4
The digits of 13967 add up to 26, and repeating that until one digit is left gives the digital root 8. The Collatz sequence (halve if even, else 3n+1) takes 89 steps to reach 1.
13967 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 13968 |
| Euler totient φ(n) | 13966 |
| Square | 195077089 |
| Cube | 2724641702063 |
| Square root | 118.182063 |
| Digit sum / digital root | 26 / 8 |
| Collatz steps to 1 | 89 |
| Scientific notation | 1.3967 × |
13967 in other forms
| Form | Value |
|---|---|
| In words | thirteen thousand nine hundred and sixty-seven |
| Binary (base 2) | 11011010001111 |
| Octal (base 8) | 33217 |
| Hexadecimal (base 16) | 368F |
| Base 3 | 201011022 |
| As time | 13967 seconds = 3 h 52 min 47 s |
Is 13967 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 3) | 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 2) | 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 8) | 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 8) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 11) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 13967 a prime number?
Yes. 13967 is divisible only by 1 and itself.
What are the factors of 13967?
1, 13967.
What is 13967 in binary?
11011010001111 (hexadecimal 368F, octal 33217).
What is the square root of 13967?
About 118.1821.
Is 13967 divisible by 3?
No. Its digits add up to 26, which is not a multiple of 3.
What is special about the number 13967?
13967 is the 1650th prime number; a happy number: repeatedly adding the squares of its digits reaches 1.