The number 1288
1288 is a composite number with 16 divisors. Its prime factorisation is × 7 × 23. Divisors (16): 1, 2, 4, 7, 8, 14, 23, 28, 46, 56, 92, 161, 184, 322, 644, 1288.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 1288: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
1288 is composite. Its prime factorisation is
- 3
The divisors add up to 2880; without 1288 itself that is 1592, so 1288 is abundant (1592 is more than 1288). Euler's totient φ(1288) = 528 numbers up to 1288 share no factor with it.
- 4
The digits of 1288 add up to 19, and repeating that until one digit is left gives the digital root 1. The Collatz sequence (halve if even, else 3n+1) takes 101 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1288 = 2^{3} \times 7 \times 23 \]1288 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 16 |
| Sum of divisors | 2880 |
| Euler totient φ(n) | 528 |
| Square | 1658944 |
| Cube | 2136719872 |
| Square root | 35.888717 (= 2√322) |
| Digit sum / digital root | 19 / 1 |
| Collatz steps to 1 | 101 |
| Scientific notation | 1.288 × |
1288 in other forms
| Form | Value |
|---|---|
| In words | one thousand two hundred and eighty-eight |
| Roman numerals | MCCLXXXVIII |
| Binary (base 2) | 10100001000 |
| Octal (base 8) | 2410 |
| Hexadecimal (base 16) | 508 |
| Base 3 | 1202201 |
| As time | 1288 seconds = 21 min 28 s |
Is 1288 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (1288 ÷ 2 = 644) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 1) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (1288 ÷ 4 = 322) | 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 4) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (1288 ÷ 7 = 184) | 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 (1288 ÷ 8 = 161) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 1) | 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 1) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 4) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 1288 a prime number?
No. 1288 = × 7 × 23, so it is divisible by 2.
What are the factors of 1288?
1, 2, 4, 7, 8, 14, 23, 28, 46, 56, 92, 161, 184, 322, 644, 1288.
What is 1288 in binary?
10100001000 (hexadecimal 508, octal 2410).
What is the square root of 1288?
About 35.8887, exactly 2√322.
What is 1288 in Roman numerals?
MCCLXXXVIII.
Is 1288 divisible by 3?
No. Its digits add up to 19, which is not a multiple of 3.
What is special about the number 1288?
1288 is a happy number: repeatedly adding the squares of its digits reaches 1.