The number 12704
12704 is a composite number with 12 divisors. Its prime factorisation is × 397. Divisors (12): 1, 2, 4, 8, 16, 32, 397, 794, 1588, 3176, 6352, 12704.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 12704: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
12704 is composite. Its prime factorisation is
- 3
The divisors add up to 25074; without 12704 itself that is 12370, so 12704 is deficient (12370 is less than 12704). Euler's totient φ(12704) = 6336 numbers up to 12704 share no factor with it.
- 4
The digits of 12704 add up to 14, and repeating that until one digit is left gives the digital root 5. The Collatz sequence (halve if even, else 3n+1) takes 32 steps to reach 1.
LaTeX source of the formulas on this page
\[ 12704 = 2^{5} \times 397 \]12704 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 25074 |
| Euler totient φ(n) | 6336 |
| Square | 161391616 |
| Cube | 2050319089664 |
| Square root | 112.712022 (= 4√794) |
| Digit sum / digital root | 14 / 5 |
| Collatz steps to 1 | 32 |
| Scientific notation | 1.2704 × |
12704 in other forms
| Form | Value |
|---|---|
| In words | twelve thousand seven hundred and four |
| Binary (base 2) | 11000110100000 |
| Octal (base 8) | 30640 |
| Hexadecimal (base 16) | 31A0 |
| Base 3 | 122102112 |
| As time | 12704 seconds = 3 h 31 min 44 s |
Is 12704 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (12704 ÷ 2 = 6352) | 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 (12704 ÷ 4 = 3176) | 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 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 (12704 ÷ 8 = 1588) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 5) | 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 10) | 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 12704 a prime number?
No. 12704 = × 397, so it is divisible by 2.
What are the factors of 12704?
1, 2, 4, 8, 16, 32, 397, 794, 1588, 3176, 6352, 12704.
What is 12704 in binary?
11000110100000 (hexadecimal 31A0, octal 30640).
What is the square root of 12704?
About 112.7120, exactly 4√794.
Is 12704 divisible by 3?
No. Its digits add up to 14, which is not a multiple of 3.
What is special about the number 12704?
12704 is a happy number: repeatedly adding the squares of its digits reaches 1.