The number 9180
9180 is a triangular number: 1 + 2 + … + 135 = 9180. Its prime factorisation is × × 5 × 17. Divisors (48): 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 17, 18, 20, 27, 30, 34 … 9180.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 9180: a triangular number: 1 + 2 + … + 135 = 9180; a Harshad number: divisible by its digit sum 18.
- 2
9180 is composite. Its prime factorisation is
- 3
The divisors add up to 30240; without 9180 itself that is 21060, so 9180 is abundant (21060 is more than 9180). Euler's totient φ(9180) = 2304 numbers up to 9180 share no factor with it.
- 4
The digits of 9180 add up to 18, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 60 steps to reach 1.
LaTeX source of the formulas on this page
\[ 9180 = 2^{2} \times 3^{3} \times 5 \times 17 \]9180 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 30240 |
| Euler totient φ(n) | 2304 |
| Square | 84272400 |
| Cube | 773620632000 |
| Square root | 95.812317 (= 6√255) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 60 |
| Scientific notation | 9.18 × |
9180 in other forms
| Form | Value |
|---|---|
| In words | nine thousand one hundred and eighty |
| Binary (base 2) | 10001111011100 |
| Octal (base 8) | 21734 |
| Hexadecimal (base 16) | 23DC |
| Base 3 | 110121000 |
| As time | 9180 seconds = 2 h 33 min 0 s |
Is 9180 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (9180 ÷ 2 = 4590) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (9180 ÷ 3 = 3060) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (9180 ÷ 4 = 2295) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (9180 ÷ 5 = 1836) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (9180 ÷ 6 = 1530) | 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 4) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (9180 ÷ 9 = 1020) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (9180 ÷ 10 = 918) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 6) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (9180 ÷ 12 = 765) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 9180 a prime number?
No. 9180 = × × 5 × 17, so it is divisible by 2.
What are the factors of 9180?
1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 17, 18, 20, 27, 30, 34, 36, 45, 51, 54, 60, 68, 85, 90, 102, 108, 135, 153, 170, 180, 204, 255, 270, 306, 340, 459, 510, 540, 612, 765, 918, 1020, 1530, 1836, 2295, 3060, 4590, 9180.
What is 9180 in binary?
10001111011100 (hexadecimal 23DC, octal 21734).
What is the square root of 9180?
About 95.8123, exactly 6√255.
Is 9180 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 9180?
9180 is a triangular number: 1 + 2 + … + 135 = 9180; a Harshad number: divisible by its digit sum 18.