The number 57984
57984 is a composite number with 32 divisors. Its prime factorisation is × 3 × 151. Divisors (32): 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 151, 192 … 57984.
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How to work it out
- 1
57984 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
57984 is composite. Its prime factorisation is
- 3
The divisors add up to 155040; without 57984 itself that is 97056, so 57984 is abundant (97056 is more than 57984). Euler's totient φ(57984) = 19200 numbers up to 57984 share no factor with it.
- 4
The digits of 57984 add up to 33, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 21 steps to reach 1.
LaTeX source of the formulas on this page
\[ 57984 = 2^{7} \times 3 \times 151 \]57984 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 32 |
| Sum of divisors | 155040 |
| Euler totient φ(n) | 19200 |
| Square | 3362144256 |
| Cube | 194950572539904 |
| Square root | 240.798671 (= 8√906) |
| Digit sum / digital root | 33 / 6 |
| Collatz steps to 1 | 21 |
| Scientific notation | 5.7984 × |
57984 in other forms
| Form | Value |
|---|---|
| In words | fifty-seven thousand nine hundred and eighty-four |
| Binary (base 2) | 1110001010000000 |
| Octal (base 8) | 161200 |
| Hexadecimal (base 16) | E280 |
| Base 3 | 2221112120 |
| As time | 57984 seconds = 16 h 6 min 24 s |
Is 57984 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (57984 ÷ 2 = 28992) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (57984 ÷ 3 = 19328) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (57984 ÷ 4 = 14496) | 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 (57984 ÷ 6 = 9664) | 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 (57984 ÷ 8 = 7248) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 6) | 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 3) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (57984 ÷ 12 = 4832) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 57984 a prime number?
No. 57984 = × 3 × 151, so it is divisible by 2.
What are the factors of 57984?
1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 151, 192, 302, 384, 453, 604, 906, 1208, 1812, 2416, 3624, 4832, 7248, 9664, 14496, 19328, 28992, 57984.
What is 57984 in binary?
1110001010000000 (hexadecimal E280, octal 161200).
What is the square root of 57984?
About 240.7987, exactly 8√906.
Is 57984 divisible by 3?
Yes. Its digits add up to 33, a multiple of 3.
What is special about the number 57984?
It is a composite number with 32 divisors.