The number 82404
82404 is a composite number with 48 divisors. Its prime factorisation is × × 7 × 109. Divisors (48): 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 27, 28, 36, 42, 54 … 82404.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 82404: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.
- 2
82404 is composite. Its prime factorisation is
- 3
The divisors add up to 246400; without 82404 itself that is 163996, so 82404 is abundant (163996 is more than 82404). Euler's totient φ(82404) = 23328 numbers up to 82404 share no factor with it.
- 4
The digits of 82404 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 63 steps to reach 1.
LaTeX source of the formulas on this page
\[ 82404 = 2^{2} \times 3^{3} \times 7 \times 109 \]82404 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 246400 |
| Euler totient φ(n) | 23328 |
| Square | 6790419216 |
| Cube | 559557705075264 |
| Square root | 287.060969 (= 6√2289) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 63 |
| Scientific notation | 8.2404 × |
82404 in other forms
| Form | Value |
|---|---|
| In words | eighty-two thousand four hundred and four |
| Binary (base 2) | 10100000111100100 |
| Octal (base 8) | 240744 |
| Hexadecimal (base 16) | 141E4 |
| Base 3 | 11012001000 |
| As time | 82404 seconds = 22 h 53 min 24 s |
Is 82404 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (82404 ÷ 2 = 41202) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (82404 ÷ 3 = 27468) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (82404 ÷ 4 = 20601) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 4) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (82404 ÷ 6 = 13734) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (82404 ÷ 7 = 11772) | 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 (82404 ÷ 9 = 9156) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 4) | 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 (82404 ÷ 12 = 6867) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 82404 a prime number?
No. 82404 = × × 7 × 109, so it is divisible by 2.
What are the factors of 82404?
1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 27, 28, 36, 42, 54, 63, 84, 108, 109, 126, 189, 218, 252, 327, 378, 436, 654, 756, 763, 981, 1308, 1526, 1962, 2289, 2943, 3052, 3924, 4578, 5886, 6867, 9156, 11772, 13734, 20601, 27468, 41202, 82404.
What is 82404 in binary?
10100000111100100 (hexadecimal 141E4, octal 240744).
What is the square root of 82404?
About 287.0610, exactly 6√2289.
Is 82404 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 82404?
82404 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.