The number 53280
53280 is a composite number with 72 divisors. Its prime factorisation is × × 5 × 37. Divisors (72): 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30 … 53280.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 53280: a Harshad number: divisible by its digit sum 18.
- 2
53280 is composite. Its prime factorisation is
- 3
The divisors add up to 186732; without 53280 itself that is 133452, so 53280 is abundant (133452 is more than 53280). Euler's totient φ(53280) = 13824 numbers up to 53280 share no factor with it.
- 4
The digits of 53280 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 184 steps to reach 1.
LaTeX source of the formulas on this page
\[ 53280 = 2^{5} \times 3^{2} \times 5 \times 37 \]53280 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 72 |
| Sum of divisors | 186732 |
| Euler totient φ(n) | 13824 |
| Square | 2838758400 |
| Cube | 151249047552000 |
| Square root | 230.824609 (= 12√370) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 184 |
| Scientific notation | 5.328 × |
53280 in other forms
| Form | Value |
|---|---|
| In words | fifty-three thousand two hundred and eighty |
| Binary (base 2) | 1101000000100000 |
| Octal (base 8) | 150040 |
| Hexadecimal (base 16) | D020 |
| Base 3 | 2201002100 |
| As time | 53280 seconds = 14 h 48 min 0 s |
Is 53280 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (53280 ÷ 2 = 26640) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (53280 ÷ 3 = 17760) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (53280 ÷ 4 = 13320) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (53280 ÷ 5 = 10656) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (53280 ÷ 6 = 8880) | 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 (53280 ÷ 8 = 6660) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (53280 ÷ 9 = 5920) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (53280 ÷ 10 = 5328) | 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 (53280 ÷ 12 = 4440) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 53280 a prime number?
No. 53280 = × × 5 × 37, so it is divisible by 2.
What are the factors of 53280?
1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 32, 36, 37, 40, 45, 48, 60, 72, 74, 80, 90, 96, 111, 120, 144, 148, 160, 180, 185, 222, 240, 288, 296, 333, 360, 370, 444, 480, 555, 592, 666, 720, 740, 888, 1110, 1184, 1332, 1440, 1480, 1665, 1776, 2220, 2664, 2960, 3330, 3552, 4440, 5328, 5920, 6660, 8880, 10656, 13320, 17760, 26640, 53280.
What is 53280 in binary?
1101000000100000 (hexadecimal D020, octal 150040).
What is the square root of 53280?
About 230.8246, exactly 12√370.
Is 53280 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 53280?
53280 is a Harshad number: divisible by its digit sum 18.