The number 1125
1125 is a composite number with 12 divisors. Its prime factorisation is × . Divisors (12): 1, 3, 5, 9, 15, 25, 45, 75, 125, 225, 375, 1125.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 1125: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 9.
- 2
1125 is composite. Its prime factorisation is
- 3
The divisors add up to 2028; without 1125 itself that is 903, so 1125 is deficient (903 is less than 1125). Euler's totient φ(1125) = 600 numbers up to 1125 share no factor with it.
- 4
The digits of 1125 add up to 9, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 44 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1125 = 3^{2} \times 5^{3} \]1125 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 2028 |
| Euler totient φ(n) | 600 |
| Square | 1265625 |
| Cube | 1423828125 |
| Square root | 33.541020 (= 15√5) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 44 |
| Scientific notation | 1.125 × |
1125 in other forms
| Form | Value |
|---|---|
| In words | one thousand one hundred and twenty-five |
| Roman numerals | MCXXV |
| Binary (base 2) | 10001100101 |
| Octal (base 8) | 2145 |
| Hexadecimal (base 16) | 465 |
| Base 3 | 1112200 |
| As time | 1125 seconds = 18 min 45 s |
Is 1125 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | No (remainder 1) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (1125 ÷ 3 = 375) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 1) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (1125 ÷ 5 = 225) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 3) | 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 5) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (1125 ÷ 9 = 125) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 5) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 3) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 9) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 1125 a prime number?
No. 1125 = × , so it is divisible by 3.
What are the factors of 1125?
1, 3, 5, 9, 15, 25, 45, 75, 125, 225, 375, 1125.
What is 1125 in binary?
10001100101 (hexadecimal 465, octal 2145).
What is the square root of 1125?
About 33.5410, exactly 15√5.
What is 1125 in Roman numerals?
MCXXV.
Is 1125 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 1125?
1125 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 9.