The number 59328
59328 is a composite number with 42 divisors. Its prime factorisation is × × 103. Divisors (42): 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72 … 59328.
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How to work it out
- 1
59328 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
59328 is composite. Its prime factorisation is
- 3
The divisors add up to 171704; without 59328 itself that is 112376, so 59328 is abundant (112376 is more than 59328). Euler's totient φ(59328) = 19584 numbers up to 59328 share no factor with it.
- 4
The digits of 59328 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 122 steps to reach 1.
LaTeX source of the formulas on this page
\[ 59328 = 2^{6} \times 3^{2} \times 103 \]59328 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 42 |
| Sum of divisors | 171704 |
| Euler totient φ(n) | 19584 |
| Square | 3519811584 |
| Cube | 208823381655552 |
| Square root | 243.573398 (= 24√103) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 122 |
| Scientific notation | 5.9328 × |
59328 in other forms
| Form | Value |
|---|---|
| In words | fifty-nine thousand three hundred and twenty-eight |
| Binary (base 2) | 1110011111000000 |
| Octal (base 8) | 163700 |
| Hexadecimal (base 16) | E7C0 |
| Base 3 | 10000101100 |
| As time | 59328 seconds = 16 h 28 min 48 s |
Is 59328 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (59328 ÷ 2 = 29664) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (59328 ÷ 3 = 19776) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (59328 ÷ 4 = 14832) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 3) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (59328 ÷ 6 = 9888) | 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 (59328 ÷ 8 = 7416) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (59328 ÷ 9 = 6592) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 8) | 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 (59328 ÷ 12 = 4944) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 59328 a prime number?
No. 59328 = × × 103, so it is divisible by 2.
What are the factors of 59328?
1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 103, 144, 192, 206, 288, 309, 412, 576, 618, 824, 927, 1236, 1648, 1854, 2472, 3296, 3708, 4944, 6592, 7416, 9888, 14832, 19776, 29664, 59328.
What is 59328 in binary?
1110011111000000 (hexadecimal E7C0, octal 163700).
What is the square root of 59328?
About 243.5734, exactly 24√103.
Is 59328 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 59328?
It is a composite number with 42 divisors.