The number 17820
17820 is a composite number with 60 divisors. Its prime factorisation is × × 5 × 11. Divisors (60): 1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 15, 18, 20, 22, 27, 30 … 17820.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 17820: a Harshad number: divisible by its digit sum 18.
- 2
17820 is composite. Its prime factorisation is
- 3
The divisors add up to 60984; without 17820 itself that is 43164, so 17820 is abundant (43164 is more than 17820). Euler's totient φ(17820) = 4320 numbers up to 17820 share no factor with it.
- 4
The digits of 17820 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 97 steps to reach 1.
LaTeX source of the formulas on this page
\[ 17820 = 2^{2} \times 3^{4} \times 5 \times 11 \]17820 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 60 |
| Sum of divisors | 60984 |
| Euler totient φ(n) | 4320 |
| Square | 317552400 |
| Cube | 5658783768000 |
| Square root | 133.491573 (= 18√55) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 97 |
| Scientific notation | 1.782 × |
17820 in other forms
| Form | Value |
|---|---|
| In words | seventeen thousand eight hundred and twenty |
| Binary (base 2) | 100010110011100 |
| Octal (base 8) | 42634 |
| Hexadecimal (base 16) | 459C |
| Base 3 | 220110000 |
| As time | 17820 seconds = 4 h 57 min 0 s |
Is 17820 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (17820 ÷ 2 = 8910) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (17820 ÷ 3 = 5940) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (17820 ÷ 4 = 4455) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (17820 ÷ 5 = 3564) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (17820 ÷ 6 = 2970) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 5) | 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 (17820 ÷ 9 = 1980) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (17820 ÷ 10 = 1782) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (17820 ÷ 11 = 1620) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (17820 ÷ 12 = 1485) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 17820 a prime number?
No. 17820 = × × 5 × 11, so it is divisible by 2.
What are the factors of 17820?
1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 15, 18, 20, 22, 27, 30, 33, 36, 44, 45, 54, 55, 60, 66, 81, 90, 99, 108, 110, 132, 135, 162, 165, 180, 198, 220, 270, 297, 324, 330, 396, 405, 495, 540, 594, 660, 810, 891, 990, 1188, 1485, 1620, 1782, 1980, 2970, 3564, 4455, 5940, 8910, 17820.
What is 17820 in binary?
100010110011100 (hexadecimal 459C, octal 42634).
What is the square root of 17820?
About 133.4916, exactly 18√55.
Is 17820 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 17820?
17820 is a Harshad number: divisible by its digit sum 18.