The number 58464
58464 is a composite number with 72 divisors. Its prime factorisation is × × 7 × 29. Divisors (72): 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 29 … 58464.
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How to work it out
- 1
58464 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
58464 is composite. Its prime factorisation is
- 3
The divisors add up to 196560; without 58464 itself that is 138096, so 58464 is abundant (138096 is more than 58464). Euler's totient φ(58464) = 16128 numbers up to 58464 share no factor with it.
- 4
The digits of 58464 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 135 steps to reach 1.
LaTeX source of the formulas on this page
\[ 58464 = 2^{5} \times 3^{2} \times 7 \times 29 \]58464 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 72 |
| Sum of divisors | 196560 |
| Euler totient φ(n) | 16128 |
| Square | 3418039296 |
| Cube | 199832249401344 |
| Square root | 241.793300 (= 12√406) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 135 |
| Scientific notation | 5.8464 × |
58464 in other forms
| Form | Value |
|---|---|
| In words | fifty-eight thousand four hundred and sixty-four |
| Binary (base 2) | 1110010001100000 |
| Octal (base 8) | 162140 |
| Hexadecimal (base 16) | E460 |
| Base 3 | 2222012100 |
| As time | 58464 seconds = 16 h 14 min 24 s |
Is 58464 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (58464 ÷ 2 = 29232) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (58464 ÷ 3 = 19488) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (58464 ÷ 4 = 14616) | 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 (58464 ÷ 6 = 9744) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (58464 ÷ 7 = 8352) | 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 (58464 ÷ 8 = 7308) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (58464 ÷ 9 = 6496) | 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 10) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (58464 ÷ 12 = 4872) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 58464 a prime number?
No. 58464 = × × 7 × 29, so it is divisible by 2.
What are the factors of 58464?
1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 29, 32, 36, 42, 48, 56, 58, 63, 72, 84, 87, 96, 112, 116, 126, 144, 168, 174, 203, 224, 232, 252, 261, 288, 336, 348, 406, 464, 504, 522, 609, 672, 696, 812, 928, 1008, 1044, 1218, 1392, 1624, 1827, 2016, 2088, 2436, 2784, 3248, 3654, 4176, 4872, 6496, 7308, 8352, 9744, 14616, 19488, 29232, 58464.
What is 58464 in binary?
1110010001100000 (hexadecimal E460, octal 162140).
What is the square root of 58464?
About 241.7933, exactly 12√406.
Is 58464 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 58464?
It is a composite number with 72 divisors.