The number 81920
81920 is a composite number with 30 divisors. Its prime factorisation is × 5. Divisors (30): 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 128, 160, 256, 320 … 81920.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 81920: a Harshad number: divisible by its digit sum 20.
- 2
81920 is composite. Its prime factorisation is
- 3
The divisors add up to 196602; without 81920 itself that is 114682, so 81920 is abundant (114682 is more than 81920). Euler's totient φ(81920) = 32768 numbers up to 81920 share no factor with it.
- 4
The digits of 81920 add up to 20, and repeating that until one digit is left gives the digital root 2. The Collatz sequence (halve if even, else 3n+1) takes 19 steps to reach 1.
LaTeX source of the formulas on this page
\[ 81920 = 2^{14} \times 5 \]81920 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 30 |
| Sum of divisors | 196602 |
| Euler totient φ(n) | 32768 |
| Square | 6710886400 |
| Cube | 549755813888000 |
| Square root | 286.216701 (= 128√5) |
| Digit sum / digital root | 20 / 2 |
| Collatz steps to 1 | 19 |
| Scientific notation | 8.192 × |
81920 in other forms
| Form | Value |
|---|---|
| In words | eighty-one thousand nine hundred and twenty |
| Binary (base 2) | 10100000000000000 |
| Octal (base 8) | 240000 |
| Hexadecimal (base 16) | 14000 |
| Base 3 | 11011101002 |
| As time | 81920 seconds = 22 h 45 min 20 s |
Is 81920 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (81920 ÷ 2 = 40960) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 2) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (81920 ÷ 4 = 20480) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (81920 ÷ 5 = 16384) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 2) | 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 (81920 ÷ 8 = 10240) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 2) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (81920 ÷ 10 = 8192) | 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 | No (remainder 8) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 81920 a prime number?
No. 81920 = × 5, so it is divisible by 2.
What are the factors of 81920?
1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 128, 160, 256, 320, 512, 640, 1024, 1280, 2048, 2560, 4096, 5120, 8192, 10240, 16384, 20480, 40960, 81920.
What is 81920 in binary?
10100000000000000 (hexadecimal 14000, octal 240000).
What is the square root of 81920?
About 286.2167, exactly 128√5.
Is 81920 divisible by 3?
No. Its digits add up to 20, which is not a multiple of 3.
What is special about the number 81920?
81920 is a Harshad number: divisible by its digit sum 20.