The number 12180
12180 is a composite number with 48 divisors. Its prime factorisation is × 3 × 5 × 7 × 29. Divisors (48): 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 29, 30 … 12180.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 12180: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 12.
- 2
12180 is composite. Its prime factorisation is
- 3
The divisors add up to 40320; without 12180 itself that is 28140, so 12180 is abundant (28140 is more than 12180). Euler's totient φ(12180) = 2688 numbers up to 12180 share no factor with it.
- 4
The digits of 12180 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 37 steps to reach 1.
LaTeX source of the formulas on this page
\[ 12180 = 2^{2} \times 3 \times 5 \times 7 \times 29 \]12180 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 40320 |
| Euler totient φ(n) | 2688 |
| Square | 148352400 |
| Cube | 1806932232000 |
| Square root | 110.363037 (= 2√3045) |
| Digit sum / digital root | 12 / 3 |
| Collatz steps to 1 | 37 |
| Scientific notation | 1.218 × |
12180 in other forms
| Form | Value |
|---|---|
| In words | twelve thousand one hundred and eighty |
| Binary (base 2) | 10111110010100 |
| Octal (base 8) | 27624 |
| Hexadecimal (base 16) | 2F94 |
| Base 3 | 121201010 |
| As time | 12180 seconds = 3 h 23 min 0 s |
Is 12180 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (12180 ÷ 2 = 6090) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (12180 ÷ 3 = 4060) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (12180 ÷ 4 = 3045) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (12180 ÷ 5 = 2436) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (12180 ÷ 6 = 2030) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (12180 ÷ 7 = 1740) | 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 4) | 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 (12180 ÷ 10 = 1218) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 3) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (12180 ÷ 12 = 1015) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 12180 a prime number?
No. 12180 = × 3 × 5 × 7 × 29, so it is divisible by 2.
What are the factors of 12180?
1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 29, 30, 35, 42, 58, 60, 70, 84, 87, 105, 116, 140, 145, 174, 203, 210, 290, 348, 406, 420, 435, 580, 609, 812, 870, 1015, 1218, 1740, 2030, 2436, 3045, 4060, 6090, 12180.
What is 12180 in binary?
10111110010100 (hexadecimal 2F94, octal 27624).
What is the square root of 12180?
About 110.3630, exactly 2√3045.
Is 12180 divisible by 3?
Yes. Its digits add up to 12, a multiple of 3.
What is special about the number 12180?
12180 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 12.