The number 57120
57120 is a composite number with 96 divisors. Its prime factorisation is × 3 × 5 × 7 × 17. Divisors (96): 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 17, 20, 21 … 57120.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 57120: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 15.
- 2
57120 is composite. Its prime factorisation is
- 3
The divisors add up to 217728; without 57120 itself that is 160608, so 57120 is abundant (160608 is more than 57120). Euler's totient φ(57120) = 12288 numbers up to 57120 share no factor with it.
- 4
The digits of 57120 add up to 15, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 34 steps to reach 1.
LaTeX source of the formulas on this page
\[ 57120 = 2^{5} \times 3 \times 5 \times 7 \times 17 \]57120 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 96 |
| Sum of divisors | 217728 |
| Euler totient φ(n) | 12288 |
| Square | 3262694400 |
| Cube | 186365104128000 |
| Square root | 238.997908 (= 4√3570) |
| Digit sum / digital root | 15 / 6 |
| Collatz steps to 1 | 34 |
| Scientific notation | 5.712 × |
57120 in other forms
| Form | Value |
|---|---|
| In words | fifty-seven thousand one hundred and twenty |
| Binary (base 2) | 1101111100100000 |
| Octal (base 8) | 157440 |
| Hexadecimal (base 16) | DF20 |
| Base 3 | 2220100120 |
| As time | 57120 seconds = 15 h 52 min 0 s |
Is 57120 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (57120 ÷ 2 = 28560) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (57120 ÷ 3 = 19040) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (57120 ÷ 4 = 14280) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (57120 ÷ 5 = 11424) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (57120 ÷ 6 = 9520) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (57120 ÷ 7 = 8160) | 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 (57120 ÷ 8 = 7140) | 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 | Yes (57120 ÷ 10 = 5712) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 8) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (57120 ÷ 12 = 4760) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 57120 a prime number?
No. 57120 = × 3 × 5 × 7 × 17, so it is divisible by 2.
What are the factors of 57120?
1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 17, 20, 21, 24, 28, 30, 32, 34, 35, 40, 42, 48, 51, 56, 60, 68, 70, 80, 84, 85, 96, 102, 105, 112, 119, 120, 136, 140, 160, 168, 170, 204, 210, 224, 238, 240, 255, 272, 280, 336, 340, 357, 408, 420, 476, 480, 510, 544, 560, 595, 672, 680, 714, 816, 840, 952, 1020, 1120, 1190, 1360, 1428, 1632, 1680, 1785, 1904, 2040, 2380, 2720, 2856, 3360, 3570, 3808, 4080, 4760, 5712, 7140, 8160, 9520, 11424, 14280, 19040, 28560, 57120.
What is 57120 in binary?
1101111100100000 (hexadecimal DF20, octal 157440).
What is the square root of 57120?
About 238.9979, exactly 4√3570.
Is 57120 divisible by 3?
Yes. Its digits add up to 15, a multiple of 3.
What is special about the number 57120?
57120 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 15.