The number 1024
1024 is a power of 2 () and a perfect square (32²). Its prime factorisation is . Divisors (11): 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 1024: a power of 2 (); a perfect square (32²).
- 2
1024 is composite. Its prime factorisation is
- 3
The divisors add up to 2047; without 1024 itself that is 1023, so 1024 is deficient (1023 is less than 1024). Euler's totient φ(1024) = 512 numbers up to 1024 share no factor with it.
- 4
The digits of 1024 add up to 7, and repeating that until one digit is left gives the digital root 7. The Collatz sequence (halve if even, else 3n+1) takes 10 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1024 = 2^{10} \]1024 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 11 |
| Sum of divisors | 2047 |
| Euler totient φ(n) | 512 |
| Square | 1048576 |
| Cube | 1073741824 |
| Square root | 32 |
| Digit sum / digital root | 7 / 7 |
| Collatz steps to 1 | 10 |
| Scientific notation | 1.024 × |
| Perfect power |
1024 in other forms
| Form | Value |
|---|---|
| In words | one thousand and twenty-four |
| Roman numerals | MXXIV |
| Binary (base 2) | 10000000000 |
| Octal (base 8) | 2000 |
| Hexadecimal (base 16) | 400 |
| Base 3 | 1101221 |
| As time | 1024 seconds = 17 min 4 s |
Is 1024 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (1024 ÷ 2 = 512) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 1) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (1024 ÷ 4 = 256) | 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 | No (remainder 4) | 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 (1024 ÷ 8 = 128) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 7) | 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 | No (remainder 4) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 1024 a prime number?
No. 1024 = , so it is divisible by 2.
What are the factors of 1024?
1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024.
What is 1024 in binary?
10000000000 (hexadecimal 400, octal 2000).
What is the square root of 1024?
32, because 32 × 32 = 1024.
What is 1024 in Roman numerals?
MXXIV.
Is 1024 divisible by 3?
No. Its digits add up to 7, which is not a multiple of 3.
What is special about the number 1024?
1024 is a power of 2 (); a perfect square (32²).