The number 82464
82464 is a composite number with 24 divisors. Its prime factorisation is × 3 × 859. Divisors (24): 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96, 859, 1718, 2577, 3436 … 82464.
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How to work it out
- 1
What is special about 82464: a Harshad number: divisible by its digit sum 24.
- 2
82464 is composite. Its prime factorisation is
- 3
The divisors add up to 216720; without 82464 itself that is 134256, so 82464 is abundant (134256 is more than 82464). Euler's totient φ(82464) = 27456 numbers up to 82464 share no factor with it.
- 4
The digits of 82464 add up to 24, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 32 steps to reach 1.
LaTeX source of the formulas on this page
\[ 82464 = 2^{5} \times 3 \times 859 \]82464 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 216720 |
| Euler totient φ(n) | 27456 |
| Square | 6800311296 |
| Cube | 560780870713344 |
| Square root | 287.165458 (= 4√5154) |
| Digit sum / digital root | 24 / 6 |
| Collatz steps to 1 | 32 |
| Scientific notation | 8.2464 × |
82464 in other forms
| Form | Value |
|---|---|
| In words | eighty-two thousand four hundred and sixty-four |
| Binary (base 2) | 10100001000100000 |
| Octal (base 8) | 241040 |
| Hexadecimal (base 16) | 14220 |
| Base 3 | 11012010020 |
| As time | 82464 seconds = 22 h 54 min 24 s |
Is 82464 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (82464 ÷ 2 = 41232) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (82464 ÷ 3 = 27488) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (82464 ÷ 4 = 20616) | 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 (82464 ÷ 6 = 13744) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 4) | 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 (82464 ÷ 8 = 10308) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 6) | 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 8) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (82464 ÷ 12 = 6872) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 82464 a prime number?
No. 82464 = × 3 × 859, so it is divisible by 2.
What are the factors of 82464?
1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96, 859, 1718, 2577, 3436, 5154, 6872, 10308, 13744, 20616, 27488, 41232, 82464.
What is 82464 in binary?
10100001000100000 (hexadecimal 14220, octal 241040).
What is the square root of 82464?
About 287.1655, exactly 4√5154.
Is 82464 divisible by 3?
Yes. Its digits add up to 24, a multiple of 3.
What is special about the number 82464?
82464 is a Harshad number: divisible by its digit sum 24.