The number 22320
22320 is a composite number with 60 divisors. Its prime factorisation is × × 5 × 31. Divisors (60): 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30 … 22320.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 22320: a Harshad number: divisible by its digit sum 9.
- 2
22320 is composite. Its prime factorisation is
- 3
The divisors add up to 77376; without 22320 itself that is 55056, so 22320 is abundant (55056 is more than 22320). Euler's totient φ(22320) = 5760 numbers up to 22320 share no factor with it.
- 4
The digits of 22320 add up to 9, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 131 steps to reach 1.
LaTeX source of the formulas on this page
\[ 22320 = 2^{4} \times 3^{2} \times 5 \times 31 \]22320 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 60 |
| Sum of divisors | 77376 |
| Euler totient φ(n) | 5760 |
| Square | 498182400 |
| Cube | 11119431168000 |
| Square root | 149.398795 (= 12√155) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 131 |
| Scientific notation | 2.232 × |
22320 in other forms
| Form | Value |
|---|---|
| In words | twenty-two thousand three hundred and twenty |
| Binary (base 2) | 101011100110000 |
| Octal (base 8) | 53460 |
| Hexadecimal (base 16) | 5730 |
| Base 3 | 1010121200 |
| As time | 22320 seconds = 6 h 12 min 0 s |
Is 22320 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (22320 ÷ 2 = 11160) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (22320 ÷ 3 = 7440) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (22320 ÷ 4 = 5580) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (22320 ÷ 5 = 4464) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (22320 ÷ 6 = 3720) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 4) | 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 (22320 ÷ 8 = 2790) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (22320 ÷ 9 = 2480) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (22320 ÷ 10 = 2232) | 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 (22320 ÷ 12 = 1860) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 22320 a prime number?
No. 22320 = × × 5 × 31, so it is divisible by 2.
What are the factors of 22320?
1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 31, 36, 40, 45, 48, 60, 62, 72, 80, 90, 93, 120, 124, 144, 155, 180, 186, 240, 248, 279, 310, 360, 372, 465, 496, 558, 620, 720, 744, 930, 1116, 1240, 1395, 1488, 1860, 2232, 2480, 2790, 3720, 4464, 5580, 7440, 11160, 22320.
What is 22320 in binary?
101011100110000 (hexadecimal 5730, octal 53460).
What is the square root of 22320?
About 149.3988, exactly 12√155.
Is 22320 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 22320?
22320 is a Harshad number: divisible by its digit sum 9.