The number 10800
10800 is a composite number with 60 divisors. Its prime factorisation is × × . Divisors (60): 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25 … 10800.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 10800: a Harshad number: divisible by its digit sum 9.
- 2
10800 is composite. Its prime factorisation is
- 3
The divisors add up to 38440; without 10800 itself that is 27640, so 10800 is abundant (27640 is more than 10800). Euler's totient φ(10800) = 2880 numbers up to 10800 share no factor with it.
- 4
The digits of 10800 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 117 steps to reach 1.
LaTeX source of the formulas on this page
\[ 10800 = 2^{4} \times 3^{3} \times 5^{2} \]10800 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 60 |
| Sum of divisors | 38440 |
| Euler totient φ(n) | 2880 |
| Square | 116640000 |
| Cube | 1259712000000 |
| Square root | 103.923048 (= 60√3) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 117 |
| Scientific notation | 1.08 × |
10800 in other forms
| Form | Value |
|---|---|
| In words | ten thousand eight hundred |
| Binary (base 2) | 10101000110000 |
| Octal (base 8) | 25060 |
| Hexadecimal (base 16) | 2A30 |
| Base 3 | 112211000 |
| As time | 10800 seconds = 3 h 0 min 0 s |
Is 10800 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (10800 ÷ 2 = 5400) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (10800 ÷ 3 = 3600) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (10800 ÷ 4 = 2700) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (10800 ÷ 5 = 2160) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (10800 ÷ 6 = 1800) | 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 (10800 ÷ 8 = 1350) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (10800 ÷ 9 = 1200) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (10800 ÷ 10 = 1080) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 9) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (10800 ÷ 12 = 900) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 10800 a prime number?
No. 10800 = × × , so it is divisible by 2.
What are the factors of 10800?
1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 27, 30, 36, 40, 45, 48, 50, 54, 60, 72, 75, 80, 90, 100, 108, 120, 135, 144, 150, 180, 200, 216, 225, 240, 270, 300, 360, 400, 432, 450, 540, 600, 675, 720, 900, 1080, 1200, 1350, 1800, 2160, 2700, 3600, 5400, 10800.
What is 10800 in binary?
10101000110000 (hexadecimal 2A30, octal 25060).
What is the square root of 10800?
About 103.9230, exactly 60√3.
Is 10800 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 10800?
10800 is a Harshad number: divisible by its digit sum 9.