The number 10784
10784 is a composite number with 12 divisors. Its prime factorisation is × 337. Divisors (12): 1, 2, 4, 8, 16, 32, 337, 674, 1348, 2696, 5392, 10784.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 10784: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
10784 is composite. Its prime factorisation is
- 3
The divisors add up to 21294; without 10784 itself that is 10510, so 10784 is deficient (10510 is less than 10784). Euler's totient φ(10784) = 5376 numbers up to 10784 share no factor with it.
- 4
The digits of 10784 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 117 steps to reach 1.
LaTeX source of the formulas on this page
\[ 10784 = 2^{5} \times 337 \]10784 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 21294 |
| Euler totient φ(n) | 5376 |
| Square | 116294656 |
| Cube | 1254121570304 |
| Square root | 103.846040 (= 4√674) |
| Digit sum / digital root | 20 / 2 |
| Collatz steps to 1 | 117 |
| Scientific notation | 1.0784 × |
10784 in other forms
| Form | Value |
|---|---|
| In words | ten thousand seven hundred and eighty-four |
| Binary (base 2) | 10101000100000 |
| Octal (base 8) | 25040 |
| Hexadecimal (base 16) | 2A20 |
| Base 3 | 112210102 |
| As time | 10784 seconds = 2 h 59 min 44 s |
Is 10784 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (10784 ÷ 2 = 5392) | 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 (10784 ÷ 4 = 2696) | 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 2) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 4) | 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 (10784 ÷ 8 = 1348) | 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 4) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 4) | 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 10784 a prime number?
No. 10784 = × 337, so it is divisible by 2.
What are the factors of 10784?
1, 2, 4, 8, 16, 32, 337, 674, 1348, 2696, 5392, 10784.
What is 10784 in binary?
10101000100000 (hexadecimal 2A20, octal 25040).
What is the square root of 10784?
About 103.8460, exactly 4√674.
Is 10784 divisible by 3?
No. Its digits add up to 20, which is not a multiple of 3.
What is special about the number 10784?
10784 is a happy number: repeatedly adding the squares of its digits reaches 1.