The number 98009
98009 is a twin prime (98009 and 98011 are both prime) and the 9419th prime number. Its only divisors are 1 and 98009.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 98009: a twin prime (98009 and 98011 are both prime); the 9419th prime number; a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
98009 is prime, so its only factors are 1 and 98009. It is the 9419th prime; the next prime is 98011 and the one before is 97987.
- 3
The divisors add up to 98010; without 98009 itself that is 1, so 98009 is deficient (1 is less than 98009). Euler's totient φ(98009) = 98008 numbers up to 98009 share no factor with it.
- 4
The digits of 98009 add up to 26, and repeating that until one digit is left gives the digital root 8. The Collatz sequence (halve if even, else 3n+1) takes 159 steps to reach 1.
98009 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 98010 |
| Euler totient φ(n) | 98008 |
| Square | 9605764081 |
| Cube | 941451331814729 |
| Square root | 313.063891 |
| Digit sum / digital root | 26 / 8 |
| Collatz steps to 1 | 159 |
| Scientific notation | 9.8009 × |
98009 in other forms
| Form | Value |
|---|---|
| In words | ninety-eight thousand and nine |
| Binary (base 2) | 10111111011011001 |
| Octal (base 8) | 277331 |
| Hexadecimal (base 16) | 17ED9 |
| Base 3 | 11222102222 |
| As time | 98009 seconds = 27 h 13 min 29 s |
Is 98009 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 4) | 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 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 8) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 9) | 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 5) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 98009 a prime number?
Yes. 98009 is divisible only by 1 and itself.
What are the factors of 98009?
1, 98009.
What is 98009 in binary?
10111111011011001 (hexadecimal 17ED9, octal 277331).
What is the square root of 98009?
About 313.0639.
Is 98009 divisible by 3?
No. Its digits add up to 26, which is not a multiple of 3.
What is special about the number 98009?
98009 is a twin prime (98009 and 98011 are both prime); the 9419th prime number; a happy number: repeatedly adding the squares of its digits reaches 1.