The number 2304
2304 is a perfect square (48²). Its prime factorisation is × . Divisors (27): 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72 … 2304.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 2304: a perfect square (48²); a Harshad number: divisible by its digit sum 9.
- 2
2304 is composite. Its prime factorisation is
- 3
The divisors add up to 6643; without 2304 itself that is 4339, so 2304 is abundant (4339 is more than 2304). Euler's totient φ(2304) = 768 numbers up to 2304 share no factor with it.
- 4
The digits of 2304 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 27 steps to reach 1.
LaTeX source of the formulas on this page
\[ 2304 = 2^{8} \times 3^{2} \]2304 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 27 |
| Sum of divisors | 6643 |
| Euler totient φ(n) | 768 |
| Square | 5308416 |
| Cube | 12230590464 |
| Square root | 48 |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 27 |
| Scientific notation | 2.304 × |
| Perfect power |
2304 in other forms
| Form | Value |
|---|---|
| In words | two thousand three hundred and four |
| Roman numerals | MMCCCIV |
| Binary (base 2) | 100100000000 |
| Octal (base 8) | 4400 |
| Hexadecimal (base 16) | 900 |
| Base 3 | 10011100 |
| As time | 2304 seconds = 38 min 24 s |
Is 2304 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (2304 ÷ 2 = 1152) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (2304 ÷ 3 = 768) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (2304 ÷ 4 = 576) | 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 (2304 ÷ 6 = 384) | 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 (2304 ÷ 8 = 288) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (2304 ÷ 9 = 256) | 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 5) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (2304 ÷ 12 = 192) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 2304 a prime number?
No. 2304 = × , so it is divisible by 2.
What are the factors of 2304?
1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 128, 144, 192, 256, 288, 384, 576, 768, 1152, 2304.
What is 2304 in binary?
100100000000 (hexadecimal 900, octal 4400).
What is the square root of 2304?
48, because 48 × 48 = 2304.
What is 2304 in Roman numerals?
MMCCCIV.
Is 2304 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 2304?
2304 is a perfect square (48²); a Harshad number: divisible by its digit sum 9.