The number 4093
4093 is a twin prime (4091 and 4093 are both prime) and the 564th prime number. Its only divisors are 1 and 4093.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 4093: a twin prime (4091 and 4093 are both prime); the 564th prime number.
- 2
4093 is prime, so its only factors are 1 and 4093. It is the 564th prime; the next prime is 4099 and the one before is 4091.
- 3
The divisors add up to 4094; without 4093 itself that is 1, so 4093 is deficient (1 is less than 4093). Euler's totient φ(4093) = 4092 numbers up to 4093 share no factor with it.
- 4
The digits of 4093 add up to 16, and repeating that until one digit is left gives the digital root 7. The Collatz sequence (halve if even, else 3n+1) takes 64 steps to reach 1.
4093 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 4094 |
| Euler totient φ(n) | 4092 |
| Square | 16752649 |
| Cube | 68568592357 |
| Square root | 63.976558 |
| Digit sum / digital root | 16 / 7 |
| Collatz steps to 1 | 64 |
| Scientific notation | 4.093 × |
4093 in other forms
| Form | Value |
|---|---|
| In words | four thousand and ninety-three |
| Binary (base 2) | 111111111101 |
| Octal (base 8) | 7775 |
| Hexadecimal (base 16) | FFD |
| Base 3 | 12121121 |
| As time | 4093 seconds = 1 h 8 min 13 s |
Is 4093 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 5) | 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 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 1) | 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 4093 a prime number?
Yes. 4093 is divisible only by 1 and itself.
What are the factors of 4093?
1, 4093.
What is 4093 in binary?
111111111101 (hexadecimal FFD, octal 7775).
What is the square root of 4093?
About 63.9766.
Is 4093 divisible by 3?
No. Its digits add up to 16, which is not a multiple of 3.
What is special about the number 4093?
4093 is a twin prime (4091 and 4093 are both prime); the 564th prime number.