The number 1409
1409 is the 223rd prime number. Its only divisors are 1 and 1409.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 1409: the 223rd prime number.
- 2
1409 is prime, so its only factors are 1 and 1409. It is the 223rd prime; the next prime is 1423 and the one before is 1399.
- 3
The divisors add up to 1410; without 1409 itself that is 1, so 1409 is deficient (1 is less than 1409). Euler's totient φ(1409) = 1408 numbers up to 1409 share no factor with it.
- 4
The digits of 1409 add up to 14, and repeating that until one digit is left gives the digital root 5. The Collatz sequence (halve if even, else 3n+1) takes 83 steps to reach 1.
1409 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 1410 |
| Euler totient φ(n) | 1408 |
| Square | 1985281 |
| Cube | 2797260929 |
| Square root | 37.536649 |
| Digit sum / digital root | 14 / 5 |
| Collatz steps to 1 | 83 |
| Scientific notation | 1.409 × |
1409 in other forms
| Form | Value |
|---|---|
| In words | one thousand four hundred and nine |
| Roman numerals | MCDIX |
| Binary (base 2) | 10110000001 |
| Octal (base 8) | 2601 |
| Hexadecimal (base 16) | 581 |
| Base 3 | 1221012 |
| As time | 1409 seconds = 23 min 29 s |
Is 1409 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 5) | 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 1) | 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 1409 a prime number?
Yes. 1409 is divisible only by 1 and itself.
What are the factors of 1409?
1, 1409.
What is 1409 in binary?
10110000001 (hexadecimal 581, octal 2601).
What is the square root of 1409?
About 37.5366.
What is 1409 in Roman numerals?
MCDIX.
Is 1409 divisible by 3?
No. Its digits add up to 14, which is not a multiple of 3.
What is special about the number 1409?
1409 is the 223rd prime number.