The number 10704
10704 is a composite number with 20 divisors. Its prime factorisation is × 3 × 223. Divisors (20): 1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 223, 446, 669, 892, 1338, 1784 … 10704.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 10704: a Harshad number: divisible by its digit sum 12.
- 2
10704 is composite. Its prime factorisation is
- 3
The divisors add up to 27776; without 10704 itself that is 17072, so 10704 is abundant (17072 is more than 10704). Euler's totient φ(10704) = 3552 numbers up to 10704 share no factor with it.
- 4
The digits of 10704 add up to 12, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 73 steps to reach 1.
LaTeX source of the formulas on this page
\[ 10704 = 2^{4} \times 3 \times 223 \]10704 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 20 |
| Sum of divisors | 27776 |
| Euler totient φ(n) | 3552 |
| Square | 114575616 |
| Cube | 1226417393664 |
| Square root | 103.460137 (= 4√669) |
| Digit sum / digital root | 12 / 3 |
| Collatz steps to 1 | 73 |
| Scientific notation | 1.0704 × |
10704 in other forms
| Form | Value |
|---|---|
| In words | ten thousand seven hundred and four |
| Binary (base 2) | 10100111010000 |
| Octal (base 8) | 24720 |
| Hexadecimal (base 16) | 29D0 |
| Base 3 | 112200110 |
| As time | 10704 seconds = 2 h 58 min 24 s |
Is 10704 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (10704 ÷ 2 = 5352) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (10704 ÷ 3 = 3568) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (10704 ÷ 4 = 2676) | 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 | Yes (10704 ÷ 6 = 1784) | 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 (10704 ÷ 8 = 1338) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 3) | 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 | Yes (10704 ÷ 12 = 892) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 10704 a prime number?
No. 10704 = × 3 × 223, so it is divisible by 2.
What are the factors of 10704?
1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 223, 446, 669, 892, 1338, 1784, 2676, 3568, 5352, 10704.
What is 10704 in binary?
10100111010000 (hexadecimal 29D0, octal 24720).
What is the square root of 10704?
About 103.4601, exactly 4√669.
Is 10704 divisible by 3?
Yes. Its digits add up to 12, a multiple of 3.
What is special about the number 10704?
10704 is a Harshad number: divisible by its digit sum 12.