The number 90180
90180 is a composite number with 48 divisors. Its prime factorisation is × × 5 × 167. Divisors (48): 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 45 … 90180.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 90180: a Harshad number: divisible by its digit sum 18.
- 2
90180 is composite. Its prime factorisation is
- 3
The divisors add up to 282240; without 90180 itself that is 192060, so 90180 is abundant (192060 is more than 90180). Euler's totient φ(90180) = 23904 numbers up to 90180 share no factor with it.
- 4
The digits of 90180 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 89 steps to reach 1.
LaTeX source of the formulas on this page
\[ 90180 = 2^{2} \times 3^{3} \times 5 \times 167 \]90180 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 282240 |
| Euler totient φ(n) | 23904 |
| Square | 8132432400 |
| Cube | 733382753832000 |
| Square root | 300.299850 (= 6√2505) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 89 |
| Scientific notation | 9.018 × |
90180 in other forms
| Form | Value |
|---|---|
| In words | ninety thousand one hundred and eighty |
| Binary (base 2) | 10110000001000100 |
| Octal (base 8) | 260104 |
| Hexadecimal (base 16) | 16044 |
| Base 3 | 11120201000 |
| As time | 90180 seconds = 25 h 3 min 0 s |
Is 90180 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (90180 ÷ 2 = 45090) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (90180 ÷ 3 = 30060) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (90180 ÷ 4 = 22545) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (90180 ÷ 5 = 18036) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (90180 ÷ 6 = 15030) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 6) | 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 (90180 ÷ 9 = 10020) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (90180 ÷ 10 = 9018) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 2) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (90180 ÷ 12 = 7515) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 90180 a prime number?
No. 90180 = × × 5 × 167, so it is divisible by 2.
What are the factors of 90180?
1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 45, 54, 60, 90, 108, 135, 167, 180, 270, 334, 501, 540, 668, 835, 1002, 1503, 1670, 2004, 2505, 3006, 3340, 4509, 5010, 6012, 7515, 9018, 10020, 15030, 18036, 22545, 30060, 45090, 90180.
What is 90180 in binary?
10110000001000100 (hexadecimal 16044, octal 260104).
What is the square root of 90180?
About 300.2999, exactly 6√2505.
Is 90180 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 90180?
90180 is a Harshad number: divisible by its digit sum 18.