The number 288
288 is a composite number with 18 divisors. Its prime factorisation is × . Divisors (18): 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96 … 288.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 288: a Harshad number: divisible by its digit sum 18.
- 2
288 is composite. Its prime factorisation is
- 3
The divisors add up to 819; without 288 itself that is 531, so 288 is abundant (531 is more than 288). Euler's totient φ(288) = 96 numbers up to 288 share no factor with it.
- 4
The digits of 288 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 24 steps to reach 1.
LaTeX source of the formulas on this page
\[ 288 = 2^{5} \times 3^{2} \]288 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 18 |
| Sum of divisors | 819 |
| Euler totient φ(n) | 96 |
| Square | 82944 |
| Cube | 23887872 |
| Square root | 16.970563 (= 12√2) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 24 |
| Scientific notation | 2.88 × |
288 in other forms
| Form | Value |
|---|---|
| In words | two hundred and eighty-eight |
| Roman numerals | CCLXXXVIII |
| Binary (base 2) | 100100000 |
| Octal (base 8) | 440 |
| Hexadecimal (base 16) | 120 |
| Base 3 | 101200 |
| As time | 288 seconds = 4 min 48 s |
Is 288 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (288 ÷ 2 = 144) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (288 ÷ 3 = 96) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (288 ÷ 4 = 72) | 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 (288 ÷ 6 = 48) | 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 (288 ÷ 8 = 36) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (288 ÷ 9 = 32) | 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 | No (remainder 2) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (288 ÷ 12 = 24) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 288 a prime number?
No. 288 = × , so it is divisible by 2.
What are the factors of 288?
1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96, 144, 288.
What is 288 in binary?
100100000 (hexadecimal 120, octal 440).
What is the square root of 288?
About 16.9706, exactly 12√2.
What is 288 in Roman numerals?
CCLXXXVIII.
Is 288 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 288?
288 is a Harshad number: divisible by its digit sum 18.