The number 53760
53760 is a composite number with 80 divisors. Its prime factorisation is × 3 × 5 × 7. Divisors (80): 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24 … 53760.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 53760: a Harshad number: divisible by its digit sum 21.
- 2
53760 is composite. Its prime factorisation is
- 3
The divisors add up to 196416; without 53760 itself that is 142656, so 53760 is abundant (142656 is more than 53760). Euler's totient φ(53760) = 12288 numbers up to 53760 share no factor with it.
- 4
The digits of 53760 add up to 21, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 47 steps to reach 1.
LaTeX source of the formulas on this page
\[ 53760 = 2^{9} \times 3 \times 5 \times 7 \]53760 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 80 |
| Sum of divisors | 196416 |
| Euler totient φ(n) | 12288 |
| Square | 2890137600 |
| Cube | 155373797376000 |
| Square root | 231.862028 (= 16√210) |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 47 |
| Scientific notation | 5.376 × |
53760 in other forms
| Form | Value |
|---|---|
| In words | fifty-three thousand seven hundred and sixty |
| Binary (base 2) | 1101001000000000 |
| Octal (base 8) | 151000 |
| Hexadecimal (base 16) | D200 |
| Base 3 | 2201202010 |
| As time | 53760 seconds = 14 h 56 min 0 s |
Is 53760 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (53760 ÷ 2 = 26880) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (53760 ÷ 3 = 17920) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (53760 ÷ 4 = 13440) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (53760 ÷ 5 = 10752) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (53760 ÷ 6 = 8960) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (53760 ÷ 7 = 7680) | 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 (53760 ÷ 8 = 6720) | 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 | Yes (53760 ÷ 10 = 5376) | 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 (53760 ÷ 12 = 4480) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 53760 a prime number?
No. 53760 = × 3 × 5 × 7, so it is divisible by 2.
What are the factors of 53760?
1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24, 28, 30, 32, 35, 40, 42, 48, 56, 60, 64, 70, 80, 84, 96, 105, 112, 120, 128, 140, 160, 168, 192, 210, 224, 240, 256, 280, 320, 336, 384, 420, 448, 480, 512, 560, 640, 672, 768, 840, 896, 960, 1120, 1280, 1344, 1536, 1680, 1792, 1920, 2240, 2560, 2688, 3360, 3584, 3840, 4480, 5376, 6720, 7680, 8960, 10752, 13440, 17920, 26880, 53760.
What is 53760 in binary?
1101001000000000 (hexadecimal D200, octal 151000).
What is the square root of 53760?
About 231.8620, exactly 16√210.
Is 53760 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 53760?
53760 is a Harshad number: divisible by its digit sum 21.