The number 1209
1209 is a composite number with 8 divisors. Its prime factorisation is 3 × 13 × 31. Divisors (8): 1, 3, 13, 31, 39, 93, 403, 1209.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 1209: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
1209 is composite. Its prime factorisation is
- 3
The divisors add up to 1792; without 1209 itself that is 583, so 1209 is deficient (583 is less than 1209). Euler's totient φ(1209) = 720 numbers up to 1209 share no factor with it.
- 4
The digits of 1209 add up to 12, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 57 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1209 = 3 \times 13 \times 31 \]
1209 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 8 |
| Sum of divisors | 1792 |
| Euler totient φ(n) | 720 |
| Square | 1461681 |
| Cube | 1767172329 |
| Square root | 34.770677 |
| Digit sum / digital root | 12 / 3 |
| Collatz steps to 1 | 57 |
| Scientific notation | 1.209 × |
1209 in other forms
| Form | Value |
|---|---|
| In words | one thousand two hundred and nine |
| Roman numerals | MCCIX |
| Binary (base 2) | 10010111001 |
| Octal (base 8) | 2271 |
| Hexadecimal (base 16) | 4B9 |
| Base 3 | 1122210 |
| As time | 1209 seconds = 20 min 9 s |
Is 1209 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 | Yes (1209 ÷ 3 = 403) | 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 3) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 5) | 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 3) | 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 9) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 1209 a prime number?
No. 1209 = 3 × 13 × 31, so it is divisible by 3.
What are the factors of 1209?
1, 3, 13, 31, 39, 93, 403, 1209.
What is 1209 in binary?
10010111001 (hexadecimal 4B9, octal 2271).
What is the square root of 1209?
About 34.7707.
What is 1209 in Roman numerals?
MCCIX.
Is 1209 divisible by 3?
Yes. Its digits add up to 12, a multiple of 3.
What is special about the number 1209?
1209 is a happy number: repeatedly adding the squares of its digits reaches 1.