The number 4993
4993 is the 668th prime number. Its only divisors are 1 and 4993.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 4993: the 668th prime number.
- 2
4993 is prime, so its only factors are 1 and 4993. It is the 668th prime; the next prime is 4999 and the one before is 4987.
- 3
The divisors add up to 4994; without 4993 itself that is 1, so 4993 is deficient (1 is less than 4993). Euler's totient φ(4993) = 4992 numbers up to 4993 share no factor with it.
- 4
The digits of 4993 add up to 25, and repeating that until one digit is left gives the digital root 7. The Collatz sequence (halve if even, else 3n+1) takes 165 steps to reach 1.
4993 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 4994 |
| Euler totient φ(n) | 4992 |
| Square | 24930049 |
| Cube | 124475734657 |
| Square root | 70.661163 |
| Digit sum / digital root | 25 / 7 |
| Collatz steps to 1 | 165 |
| Scientific notation | 4.993 × |
4993 in other forms
| Form | Value |
|---|---|
| In words | four thousand nine hundred and ninety-three |
| Binary (base 2) | 1001110000001 |
| Octal (base 8) | 11601 |
| Hexadecimal (base 16) | 1381 |
| Base 3 | 20211221 |
| As time | 4993 seconds = 1 h 23 min 13 s |
Is 4993 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 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 1) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 7) | 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 10) | 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 4993 a prime number?
Yes. 4993 is divisible only by 1 and itself.
What are the factors of 4993?
1, 4993.
What is 4993 in binary?
1001110000001 (hexadecimal 1381, octal 11601).
What is the square root of 4993?
About 70.6612.
Is 4993 divisible by 3?
No. Its digits add up to 25, which is not a multiple of 3.
What is special about the number 4993?
4993 is the 668th prime number.