The number 40009
40009 is the 4204th prime number. Its only divisors are 1 and 40009.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 40009: the 4204th prime number; a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
40009 is prime, so its only factors are 1 and 40009. It is the 4204th prime; the next prime is 40013 and the one before is 39989.
- 3
The divisors add up to 40010; without 40009 itself that is 1, so 40009 is deficient (1 is less than 40009). Euler's totient φ(40009) = 40008 numbers up to 40009 share no factor with it.
- 4
The digits of 40009 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 93 steps to reach 1.
40009 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 40010 |
| Euler totient φ(n) | 40008 |
| Square | 1600720081 |
| Cube | 64043209720729 |
| Square root | 200.022499 |
| Digit sum / digital root | 13 / 4 |
| Collatz steps to 1 | 93 |
| Scientific notation | 4.0009 × |
40009 in other forms
| Form | Value |
|---|---|
| In words | forty thousand and nine |
| Binary (base 2) | 1001110001001001 |
| Octal (base 8) | 116111 |
| Hexadecimal (base 16) | 9C49 |
| Base 3 | 2000212211 |
| As time | 40009 seconds = 11 h 6 min 49 s |
Is 40009 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 4) | 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 4) | 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 9) | 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 1) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 40009 a prime number?
Yes. 40009 is divisible only by 1 and itself.
What are the factors of 40009?
1, 40009.
What is 40009 in binary?
1001110001001001 (hexadecimal 9C49, octal 116111).
What is the square root of 40009?
About 200.0225.
Is 40009 divisible by 3?
No. Its digits add up to 13, which is not a multiple of 3.
What is special about the number 40009?
40009 is the 4204th prime number; a happy number: repeatedly adding the squares of its digits reaches 1.