The number 93001
93001 is the 8985th prime number. Its only divisors are 1 and 93001.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 93001: the 8985th prime number; a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
93001 is prime, so its only factors are 1 and 93001. It is the 8985th prime; the next prime is 93047 and the one before is 92993.
- 3
The divisors add up to 93002; without 93001 itself that is 1, so 93001 is deficient (1 is less than 93001). Euler's totient φ(93001) = 93000 numbers up to 93001 share no factor with it.
- 4
The digits of 93001 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 115 steps to reach 1.
93001 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 93002 |
| Euler totient φ(n) | 93000 |
| Square | 8649186001 |
| Cube | 804382947279001 |
| Square root | 304.960653 |
| Digit sum / digital root | 13 / 4 |
| Collatz steps to 1 | 115 |
| Scientific notation | 9.3001 × |
93001 in other forms
| Form | Value |
|---|---|
| In words | ninety-three thousand and one |
| Binary (base 2) | 10110101101001001 |
| Octal (base 8) | 265511 |
| Hexadecimal (base 16) | 16B49 |
| Base 3 | 11201120111 |
| As time | 93001 seconds = 25 h 50 min 1 s |
Is 93001 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 1) | 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 6) | 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 1) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 7) | 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 93001 a prime number?
Yes. 93001 is divisible only by 1 and itself.
What are the factors of 93001?
1, 93001.
What is 93001 in binary?
10110101101001001 (hexadecimal 16B49, octal 265511).
What is the square root of 93001?
About 304.9607.
Is 93001 divisible by 3?
No. Its digits add up to 13, which is not a multiple of 3.
What is special about the number 93001?
93001 is the 8985th prime number; a happy number: repeatedly adding the squares of its digits reaches 1.