The number 82188
82188 is a composite number with 24 divisors. Its prime factorisation is × × 761. Divisors (24): 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108, 761, 1522, 2283, 3044 … 82188.
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How to work it out
- 1
What is special about 82188: a Harshad number: divisible by its digit sum 27.
- 2
82188 is composite. Its prime factorisation is
- 3
The divisors add up to 213360; without 82188 itself that is 131172, so 82188 is abundant (131172 is more than 82188). Euler's totient φ(82188) = 27360 numbers up to 82188 share no factor with it.
- 4
The digits of 82188 add up to 27, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 151 steps to reach 1.
LaTeX source of the formulas on this page
\[ 82188 = 2^{2} \times 3^{3} \times 761 \]82188 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 213360 |
| Euler totient φ(n) | 27360 |
| Square | 6754867344 |
| Cube | 555169037268672 |
| Square root | 286.684496 (= 6√2283) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 151 |
| Scientific notation | 8.2188 × |
82188 in other forms
| Form | Value |
|---|---|
| In words | eighty-two thousand one hundred and eighty-eight |
| Binary (base 2) | 10100000100001100 |
| Octal (base 8) | 240414 |
| Hexadecimal (base 16) | 1410C |
| Base 3 | 11011202000 |
| As time | 82188 seconds = 22 h 49 min 48 s |
Is 82188 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (82188 ÷ 2 = 41094) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (82188 ÷ 3 = 27396) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (82188 ÷ 4 = 20547) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 3) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (82188 ÷ 6 = 13698) | 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 4) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (82188 ÷ 9 = 9132) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 8) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 7) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (82188 ÷ 12 = 6849) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 82188 a prime number?
No. 82188 = × × 761, so it is divisible by 2.
What are the factors of 82188?
1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108, 761, 1522, 2283, 3044, 4566, 6849, 9132, 13698, 20547, 27396, 41094, 82188.
What is 82188 in binary?
10100000100001100 (hexadecimal 1410C, octal 240414).
What is the square root of 82188?
About 286.6845, exactly 6√2283.
Is 82188 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 82188?
82188 is a Harshad number: divisible by its digit sum 27.