The number 81984
81984 is a composite number with 56 divisors. Its prime factorisation is × 3 × 7 × 61. Divisors (56): 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 32, 42, 48 … 81984.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 81984: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
81984 is composite. Its prime factorisation is
- 3
The divisors add up to 251968; without 81984 itself that is 169984, so 81984 is abundant (169984 is more than 81984). Euler's totient φ(81984) = 23040 numbers up to 81984 share no factor with it.
- 4
The digits of 81984 add up to 30, 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
\[ 81984 = 2^{6} \times 3 \times 7 \times 61 \]81984 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 56 |
| Sum of divisors | 251968 |
| Euler totient φ(n) | 23040 |
| Square | 6721376256 |
| Cube | 551045310971904 |
| Square root | 286.328483 (= 8√1281) |
| Digit sum / digital root | 30 / 3 |
| Collatz steps to 1 | 58 |
| Scientific notation | 8.1984 × |
81984 in other forms
| Form | Value |
|---|---|
| In words | eighty-one thousand nine hundred and eighty-four |
| Binary (base 2) | 10100000001000000 |
| Octal (base 8) | 240100 |
| Hexadecimal (base 16) | 14040 |
| Base 3 | 11011110110 |
| As time | 81984 seconds = 22 h 46 min 24 s |
Is 81984 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (81984 ÷ 2 = 40992) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (81984 ÷ 3 = 27328) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (81984 ÷ 4 = 20496) | 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 (81984 ÷ 6 = 13664) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (81984 ÷ 7 = 11712) | 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 (81984 ÷ 8 = 10248) | 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 1) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (81984 ÷ 12 = 6832) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 81984 a prime number?
No. 81984 = × 3 × 7 × 61, so it is divisible by 2.
What are the factors of 81984?
1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 32, 42, 48, 56, 61, 64, 84, 96, 112, 122, 168, 183, 192, 224, 244, 336, 366, 427, 448, 488, 672, 732, 854, 976, 1281, 1344, 1464, 1708, 1952, 2562, 2928, 3416, 3904, 5124, 5856, 6832, 10248, 11712, 13664, 20496, 27328, 40992, 81984.
What is 81984 in binary?
10100000001000000 (hexadecimal 14040, octal 240100).
What is the square root of 81984?
About 286.3285, exactly 8√1281.
Is 81984 divisible by 3?
Yes. Its digits add up to 30, a multiple of 3.
What is special about the number 81984?
81984 is a happy number: repeatedly adding the squares of its digits reaches 1.