The number 59904
59904 is a composite number with 60 divisors. Its prime factorisation is × × 13. Divisors (60): 1, 2, 3, 4, 6, 8, 9, 12, 13, 16, 18, 24, 26, 32, 36, 39 … 59904.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 59904: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
59904 is composite. Its prime factorisation is
- 3
The divisors add up to 186186; without 59904 itself that is 126282, so 59904 is abundant (126282 is more than 59904). Euler's totient φ(59904) = 18432 numbers up to 59904 share no factor with it.
- 4
The digits of 59904 add up to 27, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 29 steps to reach 1.
LaTeX source of the formulas on this page
\[ 59904 = 2^{9} \times 3^{2} \times 13 \]59904 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 60 |
| Sum of divisors | 186186 |
| Euler totient φ(n) | 18432 |
| Square | 3588489216 |
| Cube | 214964857995264 |
| Square root | 244.752937 (= 48√26) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 29 |
| Scientific notation | 5.9904 × |
59904 in other forms
| Form | Value |
|---|---|
| In words | fifty-nine thousand nine hundred and four |
| Binary (base 2) | 1110101000000000 |
| Octal (base 8) | 165000 |
| Hexadecimal (base 16) | EA00 |
| Base 3 | 10001011200 |
| As time | 59904 seconds = 16 h 38 min 24 s |
Is 59904 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (59904 ÷ 2 = 29952) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (59904 ÷ 3 = 19968) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (59904 ÷ 4 = 14976) | 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 (59904 ÷ 6 = 9984) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 5) | 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 (59904 ÷ 8 = 7488) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (59904 ÷ 9 = 6656) | 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 (59904 ÷ 12 = 4992) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 59904 a prime number?
No. 59904 = × × 13, so it is divisible by 2.
What are the factors of 59904?
1, 2, 3, 4, 6, 8, 9, 12, 13, 16, 18, 24, 26, 32, 36, 39, 48, 52, 64, 72, 78, 96, 104, 117, 128, 144, 156, 192, 208, 234, 256, 288, 312, 384, 416, 468, 512, 576, 624, 768, 832, 936, 1152, 1248, 1536, 1664, 1872, 2304, 2496, 3328, 3744, 4608, 4992, 6656, 7488, 9984, 14976, 19968, 29952, 59904.
What is 59904 in binary?
1110101000000000 (hexadecimal EA00, octal 165000).
What is the square root of 59904?
About 244.7529, exactly 48√26.
Is 59904 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 59904?
59904 is a happy number: repeatedly adding the squares of its digits reaches 1.