The number 82944
82944 is a perfect square (288²). Its prime factorisation is × . Divisors (55): 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54 … 82944.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 82944: a perfect square (288²); a Harshad number: divisible by its digit sum 27.
- 2
82944 is composite. Its prime factorisation is
- 3
The divisors add up to 247687; without 82944 itself that is 164743, so 82944 is abundant (164743 is more than 82944). Euler's totient φ(82944) = 27648 numbers up to 82944 share no factor with it.
- 4
The digits of 82944 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 32 steps to reach 1.
LaTeX source of the formulas on this page
\[ 82944 = 2^{10} \times 3^{4} \]82944 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 55 |
| Sum of divisors | 247687 |
| Euler totient φ(n) | 27648 |
| Square | 6879707136 |
| Cube | 570630428688384 |
| Square root | 288 |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 32 |
| Scientific notation | 8.2944 × |
| Perfect power |
82944 in other forms
| Form | Value |
|---|---|
| In words | eighty-two thousand nine hundred and forty-four |
| Binary (base 2) | 10100010000000000 |
| Octal (base 8) | 242000 |
| Hexadecimal (base 16) | 14400 |
| Base 3 | 11012210000 |
| As time | 82944 seconds = 23 h 2 min 24 s |
Is 82944 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (82944 ÷ 2 = 41472) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (82944 ÷ 3 = 27648) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (82944 ÷ 4 = 20736) | 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 (82944 ÷ 6 = 13824) | 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 | Yes (82944 ÷ 8 = 10368) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (82944 ÷ 9 = 9216) | 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 4) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (82944 ÷ 12 = 6912) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 82944 a prime number?
No. 82944 = × , so it is divisible by 2.
What are the factors of 82944?
1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 64, 72, 81, 96, 108, 128, 144, 162, 192, 216, 256, 288, 324, 384, 432, 512, 576, 648, 768, 864, 1024, 1152, 1296, 1536, 1728, 2304, 2592, 3072, 3456, 4608, 5184, 6912, 9216, 10368, 13824, 20736, 27648, 41472, 82944.
What is 82944 in binary?
10100010000000000 (hexadecimal 14400, octal 242000).
What is the square root of 82944?
288, because 288 × 288 = 82944.
Is 82944 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 82944?
82944 is a perfect square (288²); a Harshad number: divisible by its digit sum 27.