The number 409
409 is the 80th prime number. Its only divisors are 1 and 409.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 409: the 80th prime number; a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
409 is prime, so its only factors are 1 and 409. It is the 80th prime; the next prime is 419 and the one before is 401.
- 3
The divisors add up to 410; without 409 itself that is 1, so 409 is deficient (1 is less than 409). Euler's totient φ(409) = 408 numbers up to 409 share no factor with it.
- 4
The digits of 409 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 40 steps to reach 1.
409 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 410 |
| Euler totient φ(n) | 408 |
| Square | 167281 |
| Cube | 68417929 |
| Square root | 20.223748 |
| Digit sum / digital root | 13 / 4 |
| Collatz steps to 1 | 40 |
| Scientific notation | 4.09 × |
409 in other forms
| Form | Value |
|---|---|
| In words | four hundred and nine |
| Roman numerals | CDIX |
| Binary (base 2) | 110011001 |
| Octal (base 8) | 631 |
| Hexadecimal (base 16) | 199 |
| Base 3 | 120011 |
| As time | 409 seconds = 6 min 49 s |
Is 409 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 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 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 409 a prime number?
Yes. 409 is divisible only by 1 and itself.
What are the factors of 409?
1, 409.
What is 409 in binary?
110011001 (hexadecimal 199, octal 631).
What is the square root of 409?
About 20.2237.
What is 409 in Roman numerals?
CDIX.
Is 409 divisible by 3?
No. Its digits add up to 13, which is not a multiple of 3.
What is special about the number 409?
409 is the 80th prime number; a happy number: repeatedly adding the squares of its digits reaches 1.