The number 5904
5904 is a composite number with 30 divisors. Its prime factorisation is × × 41. Divisors (30): 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 41, 48, 72, 82 … 5904.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 5904: a Harshad number: divisible by its digit sum 18.
- 2
5904 is composite. Its prime factorisation is
- 3
The divisors add up to 16926; without 5904 itself that is 11022, so 5904 is abundant (11022 is more than 5904). Euler's totient φ(5904) = 1920 numbers up to 5904 share no factor with it.
- 4
The digits of 5904 add up to 18, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 23 steps to reach 1.
LaTeX source of the formulas on this page
\[ 5904 = 2^{4} \times 3^{2} \times 41 \]5904 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 30 |
| Sum of divisors | 16926 |
| Euler totient φ(n) | 1920 |
| Square | 34857216 |
| Cube | 205797003264 |
| Square root | 76.837491 (= 12√41) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 23 |
| Scientific notation | 5.904 × |
5904 in other forms
| Form | Value |
|---|---|
| In words | five thousand nine hundred and four |
| Binary (base 2) | 1011100010000 |
| Octal (base 8) | 13420 |
| Hexadecimal (base 16) | 1710 |
| Base 3 | 22002200 |
| As time | 5904 seconds = 1 h 38 min 24 s |
Is 5904 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (5904 ÷ 2 = 2952) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (5904 ÷ 3 = 1968) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (5904 ÷ 4 = 1476) | 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 (5904 ÷ 6 = 984) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 3) | 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 (5904 ÷ 8 = 738) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (5904 ÷ 9 = 656) | 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 8) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (5904 ÷ 12 = 492) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 5904 a prime number?
No. 5904 = × × 41, so it is divisible by 2.
What are the factors of 5904?
1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 41, 48, 72, 82, 123, 144, 164, 246, 328, 369, 492, 656, 738, 984, 1476, 1968, 2952, 5904.
What is 5904 in binary?
1011100010000 (hexadecimal 1710, octal 13420).
What is the square root of 5904?
About 76.8375, exactly 12√41.
Is 5904 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 5904?
5904 is a Harshad number: divisible by its digit sum 18.