The number 90001
90001 is the 8714th prime number. Its only divisors are 1 and 90001.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 90001: the 8714th prime number; a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
90001 is prime, so its only factors are 1 and 90001. It is the 8714th prime; the next prime is 90007 and the one before is 89989.
- 3
The divisors add up to 90002; without 90001 itself that is 1, so 90001 is deficient (1 is less than 90001). Euler's totient φ(90001) = 90000 numbers up to 90001 share no factor with it.
- 4
The digits of 90001 add up to 10, and repeating that until one digit is left gives the digital root 1. The Collatz sequence (halve if even, else 3n+1) takes 63 steps to reach 1.
90001 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 90002 |
| Euler totient φ(n) | 90000 |
| Square | 8100180001 |
| Cube | 729024300270001 |
| Square root | 300.001667 |
| Digit sum / digital root | 10 / 1 |
| Collatz steps to 1 | 63 |
| Scientific notation | 9.0001 × |
90001 in other forms
| Form | Value |
|---|---|
| In words | ninety thousand and one |
| Binary (base 2) | 10101111110010001 |
| Octal (base 8) | 257621 |
| Hexadecimal (base 16) | 15F91 |
| Base 3 | 11120110101 |
| As time | 90001 seconds = 25 h 0 min 1 s |
Is 90001 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 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 1) | 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 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 90001 a prime number?
Yes. 90001 is divisible only by 1 and itself.
What are the factors of 90001?
1, 90001.
What is 90001 in binary?
10101111110010001 (hexadecimal 15F91, octal 257621).
What is the square root of 90001?
About 300.0017.
Is 90001 divisible by 3?
No. Its digits add up to 10, which is not a multiple of 3.
What is special about the number 90001?
90001 is the 8714th prime number; a happy number: repeatedly adding the squares of its digits reaches 1.