The number 10404
10404 is a perfect square (102²). Its prime factorisation is × × . Divisors (27): 1, 2, 3, 4, 6, 9, 12, 17, 18, 34, 36, 51, 68, 102, 153, 204 … 10404.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 10404: a perfect square (102²); a Harshad number: divisible by its digit sum 9.
- 2
10404 is composite. Its prime factorisation is
- 3
The divisors add up to 27937; without 10404 itself that is 17533, so 10404 is abundant (17533 is more than 10404). Euler's totient φ(10404) = 3264 numbers up to 10404 share no factor with it.
- 4
The digits of 10404 add up to 9, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 179 steps to reach 1.
LaTeX source of the formulas on this page
\[ 10404 = 2^{2} \times 3^{2} \times 17^{2} \]10404 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 27 |
| Sum of divisors | 27937 |
| Euler totient φ(n) | 3264 |
| Square | 108243216 |
| Cube | 1126162419264 |
| Square root | 102 |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 179 |
| Scientific notation | 1.0404 × |
| Perfect power |
10404 in other forms
| Form | Value |
|---|---|
| In words | ten thousand four hundred and four |
| Binary (base 2) | 10100010100100 |
| Octal (base 8) | 24244 |
| Hexadecimal (base 16) | 28A4 |
| Base 3 | 112021100 |
| As time | 10404 seconds = 2 h 53 min 24 s |
Is 10404 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (10404 ÷ 2 = 5202) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (10404 ÷ 3 = 3468) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (10404 ÷ 4 = 2601) | 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 (10404 ÷ 6 = 1734) | 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 | No (remainder 4) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (10404 ÷ 9 = 1156) | 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 9) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (10404 ÷ 12 = 867) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 10404 a prime number?
No. 10404 = × × , so it is divisible by 2.
What are the factors of 10404?
1, 2, 3, 4, 6, 9, 12, 17, 18, 34, 36, 51, 68, 102, 153, 204, 289, 306, 578, 612, 867, 1156, 1734, 2601, 3468, 5202, 10404.
What is 10404 in binary?
10100010100100 (hexadecimal 28A4, octal 24244).
What is the square root of 10404?
102, because 102 × 102 = 10404.
Is 10404 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 10404?
10404 is a perfect square (102²); a Harshad number: divisible by its digit sum 9.