The number 5760
5760 is a composite number with 48 divisors. Its prime factorisation is × × 5. Divisors (48): 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30 … 5760.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 5760: a Harshad number: divisible by its digit sum 18.
- 2
5760 is composite. Its prime factorisation is
- 3
The divisors add up to 19890; without 5760 itself that is 14130, so 5760 is abundant (14130 is more than 5760). Euler's totient φ(5760) = 1536 numbers up to 5760 share no factor with it.
- 4
The digits of 5760 add up to 18, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 23 steps to reach 1.
LaTeX source of the formulas on this page
\[ 5760 = 2^{7} \times 3^{2} \times 5 \]5760 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 19890 |
| Euler totient φ(n) | 1536 |
| Square | 33177600 |
| Cube | 191102976000 |
| Square root | 75.894664 (= 24√10) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 23 |
| Scientific notation | 5.76 × |
5760 in other forms
| Form | Value |
|---|---|
| In words | five thousand seven hundred and sixty |
| Binary (base 2) | 1011010000000 |
| Octal (base 8) | 13200 |
| Hexadecimal (base 16) | 1680 |
| Base 3 | 21220100 |
| As time | 5760 seconds = 1 h 36 min 0 s |
Is 5760 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (5760 ÷ 2 = 2880) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (5760 ÷ 3 = 1920) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (5760 ÷ 4 = 1440) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (5760 ÷ 5 = 1152) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (5760 ÷ 6 = 960) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 6) | 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 (5760 ÷ 8 = 720) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (5760 ÷ 9 = 640) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (5760 ÷ 10 = 576) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 7) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (5760 ÷ 12 = 480) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 5760 a prime number?
No. 5760 = × × 5, so it is divisible by 2.
What are the factors of 5760?
1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 32, 36, 40, 45, 48, 60, 64, 72, 80, 90, 96, 120, 128, 144, 160, 180, 192, 240, 288, 320, 360, 384, 480, 576, 640, 720, 960, 1152, 1440, 1920, 2880, 5760.
What is 5760 in binary?
1011010000000 (hexadecimal 1680, octal 13200).
What is the square root of 5760?
About 75.8947, exactly 24√10.
Is 5760 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 5760?
5760 is a Harshad number: divisible by its digit sum 18.