The number 28320
28320 is a composite number with 48 divisors. Its prime factorisation is × 3 × 5 × 59. Divisors (48): 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40 … 28320.
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How to work it out
- 1
What is special about 28320: a Harshad number: divisible by its digit sum 15.
- 2
28320 is composite. Its prime factorisation is
- 3
The divisors add up to 90720; without 28320 itself that is 62400, so 28320 is abundant (62400 is more than 28320). Euler's totient φ(28320) = 7424 numbers up to 28320 share no factor with it.
- 4
The digits of 28320 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 121 steps to reach 1.
LaTeX source of the formulas on this page
\[ 28320 = 2^{5} \times 3 \times 5 \times 59 \]28320 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 90720 |
| Euler totient φ(n) | 7424 |
| Square | 802022400 |
| Cube | 22713274368000 |
| Square root | 168.285472 (= 4√1770) |
| Digit sum / digital root | 15 / 6 |
| Collatz steps to 1 | 121 |
| Scientific notation | 2.832 × |
28320 in other forms
| Form | Value |
|---|---|
| In words | twenty-eight thousand three hundred and twenty |
| Binary (base 2) | 110111010100000 |
| Octal (base 8) | 67240 |
| Hexadecimal (base 16) | 6EA0 |
| Base 3 | 1102211220 |
| As time | 28320 seconds = 7 h 52 min 0 s |
Is 28320 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (28320 ÷ 2 = 14160) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (28320 ÷ 3 = 9440) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (28320 ÷ 4 = 7080) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (28320 ÷ 5 = 5664) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (28320 ÷ 6 = 4720) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 5) | 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 (28320 ÷ 8 = 3540) | 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 (28320 ÷ 10 = 2832) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 6) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (28320 ÷ 12 = 2360) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 28320 a prime number?
No. 28320 = × 3 × 5 × 59, so it is divisible by 2.
What are the factors of 28320?
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 59, 60, 80, 96, 118, 120, 160, 177, 236, 240, 295, 354, 472, 480, 590, 708, 885, 944, 1180, 1416, 1770, 1888, 2360, 2832, 3540, 4720, 5664, 7080, 9440, 14160, 28320.
What is 28320 in binary?
110111010100000 (hexadecimal 6EA0, octal 67240).
What is the square root of 28320?
About 168.2855, exactly 4√1770.
Is 28320 divisible by 3?
Yes. Its digits add up to 15, a multiple of 3.
What is special about the number 28320?
28320 is a Harshad number: divisible by its digit sum 15.