The number 512
512 is a power of 2 (). Its prime factorisation is . Divisors (10): 1, 2, 4, 8, 16, 32, 64, 128, 256, 512.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 512: a power of 2 (); a Harshad number: divisible by its digit sum 8.
- 2
512 is composite. Its prime factorisation is
- 3
The divisors add up to 1023; without 512 itself that is 511, so 512 is deficient (511 is less than 512). Euler's totient φ(512) = 256 numbers up to 512 share no factor with it.
- 4
The digits of 512 add up to 8, and repeating that until one digit is left gives the digital root 8. The Collatz sequence (halve if even, else 3n+1) takes 9 steps to reach 1.
LaTeX source of the formulas on this page
\[ 512 = 2^{9} \]512 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 10 |
| Sum of divisors | 1023 |
| Euler totient φ(n) | 256 |
| Square | 262144 |
| Cube | 134217728 |
| Square root | 22.627417 (= 16√2) |
| Digit sum / digital root | 8 / 8 |
| Collatz steps to 1 | 9 |
| Scientific notation | 5.12 × |
| Perfect power |
512 in other forms
| Form | Value |
|---|---|
| In words | five hundred and twelve |
| Roman numerals | DXII |
| Binary (base 2) | 1000000000 |
| Octal (base 8) | 1000 |
| Hexadecimal (base 16) | 200 |
| Base 3 | 200222 |
| As time | 512 seconds = 8 min 32 s |
Is 512 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (512 ÷ 2 = 256) | 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 (512 ÷ 4 = 128) | 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 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 (512 ÷ 8 = 64) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 8) | 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 6) | 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 512 a prime number?
No. 512 = , so it is divisible by 2.
What are the factors of 512?
1, 2, 4, 8, 16, 32, 64, 128, 256, 512.
What is 512 in binary?
1000000000 (hexadecimal 200, octal 1000).
What is the square root of 512?
About 22.6274, exactly 16√2.
What is 512 in Roman numerals?
DXII.
Is 512 divisible by 3?
No. Its digits add up to 8, which is not a multiple of 3.
What is special about the number 512?
512 is a power of 2 (); a Harshad number: divisible by its digit sum 8.