The number 12090
12090 is a triangular number: 1 + 2 + … + 155 = 12090. Its prime factorisation is 2 × 3 × 5 × 13 × 31. Divisors (32): 1, 2, 3, 5, 6, 10, 13, 15, 26, 30, 31, 39, 62, 65, 78, 93 … 12090.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 12090: a triangular number: 1 + 2 + … + 155 = 12090; a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
12090 is composite. Its prime factorisation is
- 3
The divisors add up to 32256; without 12090 itself that is 20166, so 12090 is abundant (20166 is more than 12090). Euler's totient φ(12090) = 2880 numbers up to 12090 share no factor with it.
- 4
The digits of 12090 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 94 steps to reach 1.
LaTeX source of the formulas on this page
\[ 12090 = 2 \times 3 \times 5 \times 13 \times 31 \]
12090 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 32 |
| Sum of divisors | 32256 |
| Euler totient φ(n) | 2880 |
| Square | 146168100 |
| Cube | 1767172329000 |
| Square root | 109.954536 |
| Digit sum / digital root | 12 / 3 |
| Collatz steps to 1 | 94 |
| Scientific notation | 1.209 × |
12090 in other forms
| Form | Value |
|---|---|
| In words | twelve thousand and ninety |
| Binary (base 2) | 10111100111010 |
| Octal (base 8) | 27472 |
| Hexadecimal (base 16) | 2F3A |
| Base 3 | 121120210 |
| As time | 12090 seconds = 3 h 21 min 30 s |
Is 12090 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (12090 ÷ 2 = 6045) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (12090 ÷ 3 = 4030) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 2) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (12090 ÷ 5 = 2418) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (12090 ÷ 6 = 2015) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 1) | 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 2) | 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 | Yes (12090 ÷ 10 = 1209) | 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 6) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 12090 a prime number?
No. 12090 = 2 × 3 × 5 × 13 × 31, so it is divisible by 2.
What are the factors of 12090?
1, 2, 3, 5, 6, 10, 13, 15, 26, 30, 31, 39, 62, 65, 78, 93, 130, 155, 186, 195, 310, 390, 403, 465, 806, 930, 1209, 2015, 2418, 4030, 6045, 12090.
What is 12090 in binary?
10111100111010 (hexadecimal 2F3A, octal 27472).
What is the square root of 12090?
About 109.9545.
Is 12090 divisible by 3?
Yes. Its digits add up to 12, a multiple of 3.
What is special about the number 12090?
12090 is a triangular number: 1 + 2 + … + 155 = 12090; a happy number: repeatedly adding the squares of its digits reaches 1.