The number 1800
1800 is a composite number with 36 divisors. Its prime factorisation is × × . Divisors (36): 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 25, 30 … 1800.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 1800: a Harshad number: divisible by its digit sum 9.
- 2
1800 is composite. Its prime factorisation is
- 3
The divisors add up to 6045; without 1800 itself that is 4245, so 1800 is abundant (4245 is more than 1800). Euler's totient φ(1800) = 480 numbers up to 1800 share no factor with it.
- 4
The digits of 1800 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 55 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1800 = 2^{3} \times 3^{2} \times 5^{2} \]1800 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 36 |
| Sum of divisors | 6045 |
| Euler totient φ(n) | 480 |
| Square | 3240000 |
| Cube | 5832000000 |
| Square root | 42.426407 (= 30√2) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 55 |
| Scientific notation | 1.8 × |
1800 in other forms
| Form | Value |
|---|---|
| In words | one thousand eight hundred |
| Roman numerals | MDCCC |
| Binary (base 2) | 11100001000 |
| Octal (base 8) | 3410 |
| Hexadecimal (base 16) | 708 |
| Base 3 | 2110200 |
| As time | 1800 seconds = 30 min 0 s |
Is 1800 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (1800 ÷ 2 = 900) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (1800 ÷ 3 = 600) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (1800 ÷ 4 = 450) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (1800 ÷ 5 = 360) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (1800 ÷ 6 = 300) | 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 (1800 ÷ 8 = 225) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (1800 ÷ 9 = 200) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (1800 ÷ 10 = 180) | 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 (1800 ÷ 12 = 150) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 1800 a prime number?
No. 1800 = × × , so it is divisible by 2.
What are the factors of 1800?
1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 25, 30, 36, 40, 45, 50, 60, 72, 75, 90, 100, 120, 150, 180, 200, 225, 300, 360, 450, 600, 900, 1800.
What is 1800 in binary?
11100001000 (hexadecimal 708, octal 3410).
What is the square root of 1800?
About 42.4264, exactly 30√2.
What is 1800 in Roman numerals?
MDCCC.
Is 1800 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 1800?
1800 is a Harshad number: divisible by its digit sum 9.