The number 23201
23201 is a twin prime (23201 and 23203 are both prime) and the 2589th prime number. Its only divisors are 1 and 23201.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 23201: a twin prime (23201 and 23203 are both prime); the 2589th prime number.
- 2
23201 is prime, so its only factors are 1 and 23201. It is the 2589th prime; the next prime is 23203 and the one before is 23197.
- 3
The divisors add up to 23202; without 23201 itself that is 1, so 23201 is deficient (1 is less than 23201). Euler's totient φ(23201) = 23200 numbers up to 23201 share no factor with it.
- 4
The digits of 23201 add up to 8, and repeating that until one digit is left gives the digital root 8. The Collatz sequence (halve if even, else 3n+1) takes 82 steps to reach 1.
23201 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 23202 |
| Euler totient φ(n) | 23200 |
| Square | 538286401 |
| Cube | 12488782789601 |
| Square root | 152.318745 |
| Digit sum / digital root | 8 / 8 |
| Collatz steps to 1 | 82 |
| Scientific notation | 2.3201 × |
23201 in other forms
| Form | Value |
|---|---|
| In words | twenty-three thousand two hundred and one |
| Binary (base 2) | 101101010100001 |
| Octal (base 8) | 55241 |
| Hexadecimal (base 16) | 5AA1 |
| Base 3 | 1011211022 |
| As time | 23201 seconds = 6 h 26 min 41 s |
Is 23201 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 2) | 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 5) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 3) | 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 8) | 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 2) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 5) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 23201 a prime number?
Yes. 23201 is divisible only by 1 and itself.
What are the factors of 23201?
1, 23201.
What is 23201 in binary?
101101010100001 (hexadecimal 5AA1, octal 55241).
What is the square root of 23201?
About 152.3187.
Is 23201 divisible by 3?
No. Its digits add up to 8, which is not a multiple of 3.
What is special about the number 23201?
23201 is a twin prime (23201 and 23203 are both prime); the 2589th prime number.