The number 1093
1093 is a twin prime (1091 and 1093 are both prime) and the 183rd prime number. Its only divisors are 1 and 1093.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 1093: a twin prime (1091 and 1093 are both prime); the 183rd prime number; a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
1093 is prime, so its only factors are 1 and 1093. It is the 183rd prime; the next prime is 1097 and the one before is 1091.
- 3
The divisors add up to 1094; without 1093 itself that is 1, so 1093 is deficient (1 is less than 1093). Euler's totient φ(1093) = 1092 numbers up to 1093 share no factor with it.
- 4
The digits of 1093 add up to 13, and repeating that until one digit is left gives the digital root 4. The Collatz sequence (halve if even, else 3n+1) takes 31 steps to reach 1.
1093 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 1094 |
| Euler totient φ(n) | 1092 |
| Square | 1194649 |
| Cube | 1305751357 |
| Square root | 33.060551 |
| Digit sum / digital root | 13 / 4 |
| Collatz steps to 1 | 31 |
| Scientific notation | 1.093 × |
1093 in other forms
| Form | Value |
|---|---|
| In words | one thousand and ninety-three |
| Roman numerals | MXCIII |
| Binary (base 2) | 10001000101 |
| Octal (base 8) | 2105 |
| Hexadecimal (base 16) | 445 |
| Base 3 | 1111111 |
| As time | 1093 seconds = 18 min 13 s |
Is 1093 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 5) | 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 1093 a prime number?
Yes. 1093 is divisible only by 1 and itself.
What are the factors of 1093?
1, 1093.
What is 1093 in binary?
10001000101 (hexadecimal 445, octal 2105).
What is the square root of 1093?
About 33.0606.
What is 1093 in Roman numerals?
MXCIII.
Is 1093 divisible by 3?
No. Its digits add up to 13, which is not a multiple of 3.
What is special about the number 1093?
1093 is a twin prime (1091 and 1093 are both prime); the 183rd prime number; a happy number: repeatedly adding the squares of its digits reaches 1.