The number 82704
82704 is a composite number with 20 divisors. Its prime factorisation is × 3 × 1723. Divisors (20): 1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 1723, 3446, 5169, 6892, 10338, 13784 … 82704.
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How to work it out
- 1
What is special about 82704: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
82704 is composite. Its prime factorisation is
- 3
The divisors add up to 213776; without 82704 itself that is 131072, so 82704 is abundant (131072 is more than 82704). Euler's totient φ(82704) = 27552 numbers up to 82704 share no factor with it.
- 4
The digits of 82704 add up to 21, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 58 steps to reach 1.
LaTeX source of the formulas on this page
\[ 82704 = 2^{4} \times 3 \times 1723 \]82704 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 20 |
| Sum of divisors | 213776 |
| Euler totient φ(n) | 27552 |
| Square | 6839951616 |
| Cube | 565691358449664 |
| Square root | 287.583031 (= 4√5169) |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 58 |
| Scientific notation | 8.2704 × |
82704 in other forms
| Form | Value |
|---|---|
| In words | eighty-two thousand seven hundred and four |
| Binary (base 2) | 10100001100010000 |
| Octal (base 8) | 241420 |
| Hexadecimal (base 16) | 14310 |
| Base 3 | 11012110010 |
| As time | 82704 seconds = 22 h 58 min 24 s |
Is 82704 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (82704 ÷ 2 = 41352) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (82704 ÷ 3 = 27568) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (82704 ÷ 4 = 20676) | 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 (82704 ÷ 6 = 13784) | 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 | Yes (82704 ÷ 8 = 10338) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 3) | 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 6) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (82704 ÷ 12 = 6892) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 82704 a prime number?
No. 82704 = × 3 × 1723, so it is divisible by 2.
What are the factors of 82704?
1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 1723, 3446, 5169, 6892, 10338, 13784, 20676, 27568, 41352, 82704.
What is 82704 in binary?
10100001100010000 (hexadecimal 14310, octal 241420).
What is the square root of 82704?
About 287.5830, exactly 4√5169.
Is 82704 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 82704?
82704 is a happy number: repeatedly adding the squares of its digits reaches 1.