The number 9001
9001 is a twin prime (8999 and 9001 are both prime) and the 1118th prime number. Its only divisors are 1 and 9001.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 9001: a twin prime (8999 and 9001 are both prime); the 1118th prime number; a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
9001 is prime, so its only factors are 1 and 9001. It is the 1118th prime; the next prime is 9007 and the one before is 8999.
- 3
The divisors add up to 9002; without 9001 itself that is 1, so 9001 is deficient (1 is less than 9001). Euler's totient φ(9001) = 9000 numbers up to 9001 share no factor with it.
- 4
The digits of 9001 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 140 steps to reach 1.
9001 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 9002 |
| Euler totient φ(n) | 9000 |
| Square | 81018001 |
| Cube | 729243027001 |
| Square root | 94.873600 |
| Digit sum / digital root | 10 / 1 |
| Collatz steps to 1 | 140 |
| Scientific notation | 9.001 × |
9001 in other forms
| Form | Value |
|---|---|
| In words | nine thousand and one |
| Binary (base 2) | 10001100101001 |
| Octal (base 8) | 21451 |
| Hexadecimal (base 16) | 2329 |
| Base 3 | 110100101 |
| As time | 9001 seconds = 2 h 30 min 1 s |
Is 9001 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 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 3) | 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 9001 a prime number?
Yes. 9001 is divisible only by 1 and itself.
What are the factors of 9001?
1, 9001.
What is 9001 in binary?
10001100101001 (hexadecimal 2329, octal 21451).
What is the square root of 9001?
About 94.8736.
Is 9001 divisible by 3?
No. Its digits add up to 10, which is not a multiple of 3.
What is special about the number 9001?
9001 is a twin prime (8999 and 9001 are both prime); the 1118th prime number; a happy number: repeatedly adding the squares of its digits reaches 1.