The number 19993
19993 is a twin prime (19991 and 19993 are both prime) and the 2261st prime number. Its only divisors are 1 and 19993.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 19993: a twin prime (19991 and 19993 are both prime); the 2261st prime number.
- 2
19993 is prime, so its only factors are 1 and 19993. It is the 2261st prime; the next prime is 19997 and the one before is 19991.
- 3
The divisors add up to 19994; without 19993 itself that is 1, so 19993 is deficient (1 is less than 19993). Euler's totient φ(19993) = 19992 numbers up to 19993 share no factor with it.
- 4
The digits of 19993 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 66 steps to reach 1.
19993 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 19994 |
| Euler totient φ(n) | 19992 |
| Square | 399720049 |
| Cube | 7991602939657 |
| Square root | 141.396605 |
| Digit sum / digital root | 31 / 4 |
| Collatz steps to 1 | 66 |
| Scientific notation | 1.9993 × |
19993 in other forms
| Form | Value |
|---|---|
| In words | nineteen thousand nine hundred and ninety-three |
| Binary (base 2) | 100111000011001 |
| Octal (base 8) | 47031 |
| Hexadecimal (base 16) | 4E19 |
| Base 3 | 1000102111 |
| As time | 19993 seconds = 5 h 33 min 13 s |
Is 19993 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 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 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 6) | 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 19993 a prime number?
Yes. 19993 is divisible only by 1 and itself.
What are the factors of 19993?
1, 19993.
What is 19993 in binary?
100111000011001 (hexadecimal 4E19, octal 47031).
What is the square root of 19993?
About 141.3966.
Is 19993 divisible by 3?
No. Its digits add up to 31, which is not a multiple of 3.
What is special about the number 19993?
19993 is a twin prime (19991 and 19993 are both prime); the 2261st prime number.