The number 1128
1128 is a triangular number: 1 + 2 + … + 47 = 1128. Its prime factorisation is × 3 × 47. Divisors (16): 1, 2, 3, 4, 6, 8, 12, 24, 47, 94, 141, 188, 282, 376, 564, 1128.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 1128: a triangular number: 1 + 2 + … + 47 = 1128; a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 12.
- 2
1128 is composite. Its prime factorisation is
- 3
The divisors add up to 2880; without 1128 itself that is 1752, so 1128 is abundant (1752 is more than 1128). Euler's totient φ(1128) = 368 numbers up to 1128 share no factor with it.
- 4
The digits of 1128 add up to 12, 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
\[ 1128 = 2^{3} \times 3 \times 47 \]1128 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 16 |
| Sum of divisors | 2880 |
| Euler totient φ(n) | 368 |
| Square | 1272384 |
| Cube | 1435249152 |
| Square root | 33.585711 (= 2√282) |
| Digit sum / digital root | 12 / 3 |
| Collatz steps to 1 | 18 |
| Scientific notation | 1.128 × |
1128 in other forms
| Form | Value |
|---|---|
| In words | one thousand one hundred and twenty-eight |
| Roman numerals | MCXXVIII |
| Binary (base 2) | 10001101000 |
| Octal (base 8) | 2150 |
| Hexadecimal (base 16) | 468 |
| Base 3 | 1112210 |
| As time | 1128 seconds = 18 min 48 s |
Is 1128 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (1128 ÷ 2 = 564) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (1128 ÷ 3 = 376) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (1128 ÷ 4 = 282) | 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 (1128 ÷ 6 = 188) | 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 (1128 ÷ 8 = 141) | 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 | No (remainder 8) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 6) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (1128 ÷ 12 = 94) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 1128 a prime number?
No. 1128 = × 3 × 47, so it is divisible by 2.
What are the factors of 1128?
1, 2, 3, 4, 6, 8, 12, 24, 47, 94, 141, 188, 282, 376, 564, 1128.
What is 1128 in binary?
10001101000 (hexadecimal 468, octal 2150).
What is the square root of 1128?
About 33.5857, exactly 2√282.
What is 1128 in Roman numerals?
MCXXVIII.
Is 1128 divisible by 3?
Yes. Its digits add up to 12, a multiple of 3.
What is special about the number 1128?
1128 is a triangular number: 1 + 2 + … + 47 = 1128; a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 12.