The number 8192
8192 is a power of 2 (). Its prime factorisation is . Divisors (14): 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 8192: a power of 2 ().
- 2
8192 is composite. Its prime factorisation is
- 3
The divisors add up to 16383; without 8192 itself that is 8191, so 8192 is deficient (8191 is less than 8192). Euler's totient φ(8192) = 4096 numbers up to 8192 share no factor with it.
- 4
The digits of 8192 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 13 steps to reach 1.
LaTeX source of the formulas on this page
\[ 8192 = 2^{13} \]8192 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 14 |
| Sum of divisors | 16383 |
| Euler totient φ(n) | 4096 |
| Square | 67108864 |
| Cube | 549755813888 |
| Square root | 90.509668 (= 64√2) |
| Digit sum / digital root | 20 / 2 |
| Collatz steps to 1 | 13 |
| Scientific notation | 8.192 × |
| Perfect power |
8192 in other forms
| Form | Value |
|---|---|
| In words | eight thousand one hundred and ninety-two |
| Binary (base 2) | 10000000000000 |
| Octal (base 8) | 20000 |
| Hexadecimal (base 16) | 2000 |
| Base 3 | 102020102 |
| As time | 8192 seconds = 2 h 16 min 32 s |
Is 8192 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (8192 ÷ 2 = 4096) | 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 (8192 ÷ 4 = 2048) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 2) | 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 2) | 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 (8192 ÷ 8 = 1024) | 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 | No (remainder 2) | 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 | No (remainder 8) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 8192 a prime number?
No. 8192 = , so it is divisible by 2.
What are the factors of 8192?
1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192.
What is 8192 in binary?
10000000000000 (hexadecimal 2000, octal 20000).
What is the square root of 8192?
About 90.5097, exactly 64√2.
Is 8192 divisible by 3?
No. Its digits add up to 20, which is not a multiple of 3.
What is special about the number 8192?
8192 is a power of 2 ().