The number 1309
1309 is a composite number with 8 divisors. Its prime factorisation is 7 × 11 × 17. Divisors (8): 1, 7, 11, 17, 77, 119, 187, 1309.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 1309: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
1309 is composite. Its prime factorisation is
- 3
The divisors add up to 1728; without 1309 itself that is 419, so 1309 is deficient (419 is less than 1309). Euler's totient φ(1309) = 960 numbers up to 1309 share no factor with it.
- 4
The digits of 1309 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 145 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1309 = 7 \times 11 \times 17 \]
1309 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 8 |
| Sum of divisors | 1728 |
| Euler totient φ(n) | 960 |
| Square | 1713481 |
| Cube | 2242946629 |
| Square root | 36.180105 |
| Digit sum / digital root | 13 / 4 |
| Collatz steps to 1 | 145 |
| Scientific notation | 1.309 × |
1309 in other forms
| Form | Value |
|---|---|
| In words | one thousand three hundred and nine |
| Roman numerals | MCCCIX |
| Binary (base 2) | 10100011101 |
| Octal (base 8) | 2435 |
| Hexadecimal (base 16) | 51D |
| Base 3 | 1210111 |
| As time | 1309 seconds = 21 min 49 s |
Is 1309 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 | Yes (1309 ÷ 7 = 187) | 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 5) | 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 | Yes (1309 ÷ 11 = 119) | 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 1309 a prime number?
No. 1309 = 7 × 11 × 17, so it is divisible by 7.
What are the factors of 1309?
1, 7, 11, 17, 77, 119, 187, 1309.
What is 1309 in binary?
10100011101 (hexadecimal 51D, octal 2435).
What is the square root of 1309?
About 36.1801.
What is 1309 in Roman numerals?
MCCCIX.
Is 1309 divisible by 3?
No. Its digits add up to 13, which is not a multiple of 3.
What is special about the number 1309?
1309 is a happy number: repeatedly adding the squares of its digits reaches 1.