The number 57792
57792 is a composite number with 56 divisors. Its prime factorisation is × 3 × 7 × 43. Divisors (56): 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 32, 42, 43 … 57792.
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How to work it out
- 1
What is special about 57792: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
57792 is composite. Its prime factorisation is
- 3
The divisors add up to 178816; without 57792 itself that is 121024, so 57792 is abundant (121024 is more than 57792). Euler's totient φ(57792) = 16128 numbers up to 57792 share no factor with it.
- 4
The digits of 57792 add up to 30, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 122 steps to reach 1.
LaTeX source of the formulas on this page
\[ 57792 = 2^{6} \times 3 \times 7 \times 43 \]57792 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 56 |
| Sum of divisors | 178816 |
| Euler totient φ(n) | 16128 |
| Square | 3339915264 |
| Cube | 193020382937088 |
| Square root | 240.399667 (= 8√903) |
| Digit sum / digital root | 30 / 3 |
| Collatz steps to 1 | 122 |
| Scientific notation | 5.7792 × |
57792 in other forms
| Form | Value |
|---|---|
| In words | fifty-seven thousand seven hundred and ninety-two |
| Binary (base 2) | 1110000111000000 |
| Octal (base 8) | 160700 |
| Hexadecimal (base 16) | E1C0 |
| Base 3 | 2221021110 |
| As time | 57792 seconds = 16 h 3 min 12 s |
Is 57792 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (57792 ÷ 2 = 28896) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (57792 ÷ 3 = 19264) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (57792 ÷ 4 = 14448) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 2) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (57792 ÷ 6 = 9632) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (57792 ÷ 7 = 8256) | 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 (57792 ÷ 8 = 7224) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 3) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 2) | 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 (57792 ÷ 12 = 4816) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 57792 a prime number?
No. 57792 = × 3 × 7 × 43, so it is divisible by 2.
What are the factors of 57792?
1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 32, 42, 43, 48, 56, 64, 84, 86, 96, 112, 129, 168, 172, 192, 224, 258, 301, 336, 344, 448, 516, 602, 672, 688, 903, 1032, 1204, 1344, 1376, 1806, 2064, 2408, 2752, 3612, 4128, 4816, 7224, 8256, 9632, 14448, 19264, 28896, 57792.
What is 57792 in binary?
1110000111000000 (hexadecimal E1C0, octal 160700).
What is the square root of 57792?
About 240.3997, exactly 8√903.
Is 57792 divisible by 3?
Yes. Its digits add up to 30, a multiple of 3.
What is special about the number 57792?
57792 is a happy number: repeatedly adding the squares of its digits reaches 1.