The number 10240
10240 is a composite number with 24 divisors. Its prime factorisation is × 5. Divisors (24): 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 128, 160, 256, 320 … 10240.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
10240 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
10240 is composite. Its prime factorisation is
- 3
The divisors add up to 24570; without 10240 itself that is 14330, so 10240 is abundant (14330 is more than 10240). Euler's totient φ(10240) = 4096 numbers up to 10240 share no factor with it.
- 4
The digits of 10240 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 16 steps to reach 1.
LaTeX source of the formulas on this page
\[ 10240 = 2^{11} \times 5 \]10240 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 24570 |
| Euler totient φ(n) | 4096 |
| Square | 104857600 |
| Cube | 1073741824000 |
| Square root | 101.192885 (= 32√10) |
| Digit sum / digital root | 7 / 7 |
| Collatz steps to 1 | 16 |
| Scientific notation | 1.024 × |
10240 in other forms
| Form | Value |
|---|---|
| In words | ten thousand two hundred and forty |
| Binary (base 2) | 10100000000000 |
| Octal (base 8) | 24000 |
| Hexadecimal (base 16) | 2800 |
| Base 3 | 112001021 |
| As time | 10240 seconds = 2 h 50 min 40 s |
Is 10240 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (10240 ÷ 2 = 5120) | 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 (10240 ÷ 4 = 2560) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (10240 ÷ 5 = 2048) | 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 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 (10240 ÷ 8 = 1280) | 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 | Yes (10240 ÷ 10 = 1024) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 10) | 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 10240 a prime number?
No. 10240 = × 5, so it is divisible by 2.
What are the factors of 10240?
1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 128, 160, 256, 320, 512, 640, 1024, 1280, 2048, 2560, 5120, 10240.
What is 10240 in binary?
10100000000000 (hexadecimal 2800, octal 24000).
What is the square root of 10240?
About 101.1929, exactly 32√10.
Is 10240 divisible by 3?
No. Its digits add up to 7, which is not a multiple of 3.
What is special about the number 10240?
It is a composite number with 24 divisors.