The number 21600
21600 is a composite number with 72 divisors. Its prime factorisation is × × . Divisors (72): 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25 … 21600.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 21600: a Harshad number: divisible by its digit sum 9.
- 2
21600 is composite. Its prime factorisation is
- 3
The divisors add up to 78120; without 21600 itself that is 56520, so 21600 is abundant (56520 is more than 21600). Euler's totient φ(21600) = 5760 numbers up to 21600 share no factor with it.
- 4
The digits of 21600 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 118 steps to reach 1.
LaTeX source of the formulas on this page
\[ 21600 = 2^{5} \times 3^{3} \times 5^{2} \]21600 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 72 |
| Sum of divisors | 78120 |
| Euler totient φ(n) | 5760 |
| Square | 466560000 |
| Cube | 10077696000000 |
| Square root | 146.969385 (= 60√6) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 118 |
| Scientific notation | 2.16 × |
21600 in other forms
| Form | Value |
|---|---|
| In words | twenty-one thousand six hundred |
| Binary (base 2) | 101010001100000 |
| Octal (base 8) | 52140 |
| Hexadecimal (base 16) | 5460 |
| Base 3 | 1002122000 |
| As time | 21600 seconds = 6 h 0 min 0 s |
Is 21600 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (21600 ÷ 2 = 10800) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (21600 ÷ 3 = 7200) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (21600 ÷ 4 = 5400) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (21600 ÷ 5 = 4320) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (21600 ÷ 6 = 3600) | 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 (21600 ÷ 8 = 2700) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (21600 ÷ 9 = 2400) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (21600 ÷ 10 = 2160) | 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 (21600 ÷ 12 = 1800) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 21600 a prime number?
No. 21600 = × × , so it is divisible by 2.
What are the factors of 21600?
1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 27, 30, 32, 36, 40, 45, 48, 50, 54, 60, 72, 75, 80, 90, 96, 100, 108, 120, 135, 144, 150, 160, 180, 200, 216, 225, 240, 270, 288, 300, 360, 400, 432, 450, 480, 540, 600, 675, 720, 800, 864, 900, 1080, 1200, 1350, 1440, 1800, 2160, 2400, 2700, 3600, 4320, 5400, 7200, 10800, 21600.
What is 21600 in binary?
101010001100000 (hexadecimal 5460, octal 52140).
What is the square root of 21600?
About 146.9694, exactly 60√6.
Is 21600 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 21600?
21600 is a Harshad number: divisible by its digit sum 9.