The number 1088
1088 is a composite number with 14 divisors. Its prime factorisation is × 17. Divisors (14): 1, 2, 4, 8, 16, 17, 32, 34, 64, 68, 136, 272, 544, 1088.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 1088: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 17.
- 2
1088 is composite. Its prime factorisation is
- 3
The divisors add up to 2286; without 1088 itself that is 1198, so 1088 is abundant (1198 is more than 1088). Euler's totient φ(1088) = 512 numbers up to 1088 share no factor with it.
- 4
The digits of 1088 add up to 17, and repeating that until one digit is left gives the digital root 8. The Collatz sequence (halve if even, else 3n+1) takes 18 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1088 = 2^{6} \times 17 \]1088 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 14 |
| Sum of divisors | 2286 |
| Euler totient φ(n) | 512 |
| Square | 1183744 |
| Cube | 1287913472 |
| Square root | 32.984845 (= 8√17) |
| Digit sum / digital root | 17 / 8 |
| Collatz steps to 1 | 18 |
| Scientific notation | 1.088 × |
1088 in other forms
| Form | Value |
|---|---|
| In words | one thousand and eighty-eight |
| Roman numerals | MLXXXVIII |
| Binary (base 2) | 10001000000 |
| Octal (base 8) | 2100 |
| Hexadecimal (base 16) | 440 |
| Base 3 | 1111022 |
| As time | 1088 seconds = 18 min 8 s |
Is 1088 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (1088 ÷ 2 = 544) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 2) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (1088 ÷ 4 = 272) | 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 | No (remainder 2) | 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 (1088 ÷ 8 = 136) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 8) | 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 10) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 8) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 1088 a prime number?
No. 1088 = × 17, so it is divisible by 2.
What are the factors of 1088?
1, 2, 4, 8, 16, 17, 32, 34, 64, 68, 136, 272, 544, 1088.
What is 1088 in binary?
10001000000 (hexadecimal 440, octal 2100).
What is the square root of 1088?
About 32.9848, exactly 8√17.
What is 1088 in Roman numerals?
MLXXXVIII.
Is 1088 divisible by 3?
No. Its digits add up to 17, which is not a multiple of 3.
What is special about the number 1088?
1088 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 17.