The number 1200
1200 is a composite number with 30 divisors. Its prime factorisation is × 3 × . Divisors (30): 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 40 … 1200.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 1200: a Harshad number: divisible by its digit sum 3.
- 2
1200 is composite. Its prime factorisation is
- 3
The divisors add up to 3844; without 1200 itself that is 2644, so 1200 is abundant (2644 is more than 1200). Euler's totient φ(1200) = 320 numbers up to 1200 share no factor with it.
- 4
The digits of 1200 add up to 3, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 18 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1200 = 2^{4} \times 3 \times 5^{2} \]1200 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 30 |
| Sum of divisors | 3844 |
| Euler totient φ(n) | 320 |
| Square | 1440000 |
| Cube | 1728000000 |
| Square root | 34.641016 (= 20√3) |
| Digit sum / digital root | 3 / 3 |
| Collatz steps to 1 | 18 |
| Scientific notation | 1.2 × |
1200 in other forms
| Form | Value |
|---|---|
| In words | one thousand two hundred |
| Roman numerals | MCC |
| Binary (base 2) | 10010110000 |
| Octal (base 8) | 2260 |
| Hexadecimal (base 16) | 4B0 |
| Base 3 | 1122110 |
| As time | 1200 seconds = 20 min 0 s |
Is 1200 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (1200 ÷ 2 = 600) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (1200 ÷ 3 = 400) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (1200 ÷ 4 = 300) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (1200 ÷ 5 = 240) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (1200 ÷ 6 = 200) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 3) | 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 (1200 ÷ 8 = 150) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 3) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (1200 ÷ 10 = 120) | 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 (1200 ÷ 12 = 100) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 1200 a prime number?
No. 1200 = × 3 × , so it is divisible by 2.
What are the factors of 1200?
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 40, 48, 50, 60, 75, 80, 100, 120, 150, 200, 240, 300, 400, 600, 1200.
What is 1200 in binary?
10010110000 (hexadecimal 4B0, octal 2260).
What is the square root of 1200?
About 34.6410, exactly 20√3.
What is 1200 in Roman numerals?
MCC.
Is 1200 divisible by 3?
Yes. Its digits add up to 3, a multiple of 3.
What is special about the number 1200?
1200 is a Harshad number: divisible by its digit sum 3.