The number 20320
20320 is a composite number with 24 divisors. Its prime factorisation is × 5 × 127. Divisors (24): 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 80, 127, 160, 254, 508, 635 … 20320.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
20320 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
20320 is composite. Its prime factorisation is
- 3
The divisors add up to 48384; without 20320 itself that is 28064, so 20320 is abundant (28064 is more than 20320). Euler's totient φ(20320) = 8064 numbers up to 20320 share no factor with it.
- 4
The digits of 20320 add up to 7, and repeating that until one digit is left gives the digital root 7. The Collatz sequence (halve if even, else 3n+1) takes 35 steps to reach 1.
LaTeX source of the formulas on this page
\[ 20320 = 2^{5} \times 5 \times 127 \]20320 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 48384 |
| Euler totient φ(n) | 8064 |
| Square | 412902400 |
| Cube | 8390176768000 |
| Square root | 142.548237 (= 4√1270) |
| Digit sum / digital root | 7 / 7 |
| Collatz steps to 1 | 35 |
| Scientific notation | 2.032 × |
20320 in other forms
| Form | Value |
|---|---|
| In words | twenty thousand three hundred and twenty |
| Binary (base 2) | 100111101100000 |
| Octal (base 8) | 47540 |
| Hexadecimal (base 16) | 4F60 |
| Base 3 | 1000212121 |
| As time | 20320 seconds = 5 h 38 min 40 s |
Is 20320 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (20320 ÷ 2 = 10160) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 1) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (20320 ÷ 4 = 5080) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (20320 ÷ 5 = 4064) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 4) | 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 (20320 ÷ 8 = 2540) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 7) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (20320 ÷ 10 = 2032) | 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 | No (remainder 4) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 20320 a prime number?
No. 20320 = × 5 × 127, so it is divisible by 2.
What are the factors of 20320?
1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 80, 127, 160, 254, 508, 635, 1016, 1270, 2032, 2540, 4064, 5080, 10160, 20320.
What is 20320 in binary?
100111101100000 (hexadecimal 4F60, octal 47540).
What is the square root of 20320?
About 142.5482, exactly 4√1270.
Is 20320 divisible by 3?
No. Its digits add up to 7, which is not a multiple of 3.
What is special about the number 20320?
It is a composite number with 24 divisors.