The number 23104
23104 is a perfect square (152²). Its prime factorisation is × . Divisors (21): 1, 2, 4, 8, 16, 19, 32, 38, 64, 76, 152, 304, 361, 608, 722, 1216 … 23104.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 23104: a perfect square (152²).
- 2
23104 is composite. Its prime factorisation is
- 3
The divisors add up to 48387; without 23104 itself that is 25283, so 23104 is abundant (25283 is more than 23104). Euler's totient φ(23104) = 10944 numbers up to 23104 share no factor with it.
- 4
The digits of 23104 add up to 10, and repeating that until one digit is left gives the digital root 1. The Collatz sequence (halve if even, else 3n+1) takes 51 steps to reach 1.
LaTeX source of the formulas on this page
\[ 23104 = 2^{6} \times 19^{2} \]23104 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 21 |
| Sum of divisors | 48387 |
| Euler totient φ(n) | 10944 |
| Square | 533794816 |
| Cube | 12332795428864 |
| Square root | 152 |
| Digit sum / digital root | 10 / 1 |
| Collatz steps to 1 | 51 |
| Scientific notation | 2.3104 × |
| Perfect power |
23104 in other forms
| Form | Value |
|---|---|
| In words | twenty-three thousand one hundred and four |
| Binary (base 2) | 101101001000000 |
| Octal (base 8) | 55100 |
| Hexadecimal (base 16) | 5A40 |
| Base 3 | 1011200201 |
| As time | 23104 seconds = 6 h 25 min 4 s |
Is 23104 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (23104 ÷ 2 = 11552) | 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 (23104 ÷ 4 = 5776) | 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 4) | 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 (23104 ÷ 8 = 2888) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 1) | 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 4) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 23104 a prime number?
No. 23104 = × , so it is divisible by 2.
What are the factors of 23104?
1, 2, 4, 8, 16, 19, 32, 38, 64, 76, 152, 304, 361, 608, 722, 1216, 1444, 2888, 5776, 11552, 23104.
What is 23104 in binary?
101101001000000 (hexadecimal 5A40, octal 55100).
What is the square root of 23104?
152, because 152 × 152 = 23104.
Is 23104 divisible by 3?
No. Its digits add up to 10, which is not a multiple of 3.
What is special about the number 23104?
23104 is a perfect square (152²).