The number 1188
1188 is a composite number with 24 divisors. Its prime factorisation is × × 11. Divisors (24): 1, 2, 3, 4, 6, 9, 11, 12, 18, 22, 27, 33, 36, 44, 54, 66 … 1188.
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How to work it out
- 1
What is special about 1188: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.
- 2
1188 is composite. Its prime factorisation is
- 3
The divisors add up to 3360; without 1188 itself that is 2172, so 1188 is abundant (2172 is more than 1188). Euler's totient φ(1188) = 360 numbers up to 1188 share no factor with it.
- 4
The digits of 1188 add up to 18, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 75 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1188 = 2^{2} \times 3^{3} \times 11 \]1188 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 3360 |
| Euler totient φ(n) | 360 |
| Square | 1411344 |
| Cube | 1676676672 |
| Square root | 34.467376 (= 6√33) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 75 |
| Scientific notation | 1.188 × |
1188 in other forms
| Form | Value |
|---|---|
| In words | one thousand one hundred and eighty-eight |
| Roman numerals | MCLXXXVIII |
| Binary (base 2) | 10010100100 |
| Octal (base 8) | 2244 |
| Hexadecimal (base 16) | 4A4 |
| Base 3 | 1122000 |
| As time | 1188 seconds = 19 min 48 s |
Is 1188 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (1188 ÷ 2 = 594) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (1188 ÷ 3 = 396) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (1188 ÷ 4 = 297) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 3) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (1188 ÷ 6 = 198) | 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 | No (remainder 4) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (1188 ÷ 9 = 132) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 8) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (1188 ÷ 11 = 108) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (1188 ÷ 12 = 99) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 1188 a prime number?
No. 1188 = × × 11, so it is divisible by 2.
What are the factors of 1188?
1, 2, 3, 4, 6, 9, 11, 12, 18, 22, 27, 33, 36, 44, 54, 66, 99, 108, 132, 198, 297, 396, 594, 1188.
What is 1188 in binary?
10010100100 (hexadecimal 4A4, octal 2244).
What is the square root of 1188?
About 34.4674, exactly 6√33.
What is 1188 in Roman numerals?
MCLXXXVIII.
Is 1188 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 1188?
1188 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.