The number 10993
10993 is the 1335th prime number. Its only divisors are 1 and 10993.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 10993: the 1335th prime number.
- 2
10993 is prime, so its only factors are 1 and 10993. It is the 1335th prime; the next prime is 11003 and the one before is 10987.
- 3
The divisors add up to 10994; without 10993 itself that is 1, so 10993 is deficient (1 is less than 10993). Euler's totient φ(10993) = 10992 numbers up to 10993 share no factor with it.
- 4
The digits of 10993 add up to 22, and repeating that until one digit is left gives the digital root 4. The Collatz sequence (halve if even, else 3n+1) takes 130 steps to reach 1.
10993 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 10994 |
| Euler totient φ(n) | 10992 |
| Square | 120846049 |
| Cube | 1328460616657 |
| Square root | 104.847508 |
| Digit sum / digital root | 22 / 4 |
| Collatz steps to 1 | 130 |
| Scientific notation | 1.0993 × |
10993 in other forms
| Form | Value |
|---|---|
| In words | ten thousand nine hundred and ninety-three |
| Binary (base 2) | 10101011110001 |
| Octal (base 8) | 25361 |
| Hexadecimal (base 16) | 2AF1 |
| Base 3 | 120002011 |
| As time | 10993 seconds = 3 h 3 min 13 s |
Is 10993 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 1) | 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 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 1) | 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 3) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 4) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 1) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 10993 a prime number?
Yes. 10993 is divisible only by 1 and itself.
What are the factors of 10993?
1, 10993.
What is 10993 in binary?
10101011110001 (hexadecimal 2AF1, octal 25361).
What is the square root of 10993?
About 104.8475.
Is 10993 divisible by 3?
No. Its digits add up to 22, which is not a multiple of 3.
What is special about the number 10993?
10993 is the 1335th prime number.