The number 88320
88320 is a composite number with 72 divisors. Its prime factorisation is × 3 × 5 × 23. Divisors (72): 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 23, 24, 30, 32 … 88320.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
88320 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
88320 is composite. Its prime factorisation is
- 3
The divisors add up to 294336; without 88320 itself that is 206016, so 88320 is abundant (206016 is more than 88320). Euler's totient φ(88320) = 22528 numbers up to 88320 share no factor with it.
- 4
The digits of 88320 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 133 steps to reach 1.
LaTeX source of the formulas on this page
\[ 88320 = 2^{8} \times 3 \times 5 \times 23 \]88320 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 72 |
| Sum of divisors | 294336 |
| Euler totient φ(n) | 22528 |
| Square | 7800422400 |
| Cube | 688933306368000 |
| Square root | 297.186810 (= 16√345) |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 133 |
| Scientific notation | 8.832 × |
88320 in other forms
| Form | Value |
|---|---|
| In words | eighty-eight thousand three hundred and twenty |
| Binary (base 2) | 10101100100000000 |
| Octal (base 8) | 254400 |
| Hexadecimal (base 16) | 15900 |
| Base 3 | 11111011010 |
| As time | 88320 seconds = 24 h 32 min 0 s |
Is 88320 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (88320 ÷ 2 = 44160) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (88320 ÷ 3 = 29440) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (88320 ÷ 4 = 22080) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (88320 ÷ 5 = 17664) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (88320 ÷ 6 = 14720) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 1) | 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 (88320 ÷ 8 = 11040) | 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 (88320 ÷ 10 = 8832) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 1) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (88320 ÷ 12 = 7360) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 88320 a prime number?
No. 88320 = × 3 × 5 × 23, so it is divisible by 2.
What are the factors of 88320?
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 23, 24, 30, 32, 40, 46, 48, 60, 64, 69, 80, 92, 96, 115, 120, 128, 138, 160, 184, 192, 230, 240, 256, 276, 320, 345, 368, 384, 460, 480, 552, 640, 690, 736, 768, 920, 960, 1104, 1280, 1380, 1472, 1840, 1920, 2208, 2760, 2944, 3680, 3840, 4416, 5520, 5888, 7360, 8832, 11040, 14720, 17664, 22080, 29440, 44160, 88320.
What is 88320 in binary?
10101100100000000 (hexadecimal 15900, octal 254400).
What is the square root of 88320?
About 297.1868, exactly 16√345.
Is 88320 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 88320?
It is a composite number with 72 divisors.