The number 3209
3209 is the 454th prime number. Its only divisors are 1 and 3209.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 3209: the 454th prime number; a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
3209 is prime, so its only factors are 1 and 3209. It is the 454th prime; the next prime is 3217 and the one before is 3203.
- 3
The divisors add up to 3210; without 3209 itself that is 1, so 3209 is deficient (1 is less than 3209). Euler's totient φ(3209) = 3208 numbers up to 3209 share no factor with it.
- 4
The digits of 3209 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 74 steps to reach 1.
3209 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 3210 |
| Euler totient φ(n) | 3208 |
| Square | 10297681 |
| Cube | 33045258329 |
| Square root | 56.648036 |
| Digit sum / digital root | 14 / 5 |
| Collatz steps to 1 | 74 |
| Scientific notation | 3.209 × |
3209 in other forms
| Form | Value |
|---|---|
| In words | three thousand two hundred and nine |
| Roman numerals | MMMCCIX |
| Binary (base 2) | 110010001001 |
| Octal (base 8) | 6211 |
| Hexadecimal (base 16) | C89 |
| Base 3 | 11101212 |
| As time | 3209 seconds = 53 min 29 s |
Is 3209 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 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 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 8) | 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 3209 a prime number?
Yes. 3209 is divisible only by 1 and itself.
What are the factors of 3209?
1, 3209.
What is 3209 in binary?
110010001001 (hexadecimal C89, octal 6211).
What is the square root of 3209?
About 56.6480.
What is 3209 in Roman numerals?
MMMCCIX.
Is 3209 divisible by 3?
No. Its digits add up to 14, which is not a multiple of 3.
What is special about the number 3209?
3209 is the 454th prime number; a happy number: repeatedly adding the squares of its digits reaches 1.