The number 11025
11025 is a perfect square (105²). Its prime factorisation is × × . Divisors (27): 1, 3, 5, 7, 9, 15, 21, 25, 35, 45, 49, 63, 75, 105, 147, 175 … 11025.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 11025: a perfect square (105²); a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 9.
- 2
11025 is composite. Its prime factorisation is
- 3
The divisors add up to 22971; without 11025 itself that is 11946, so 11025 is abundant (11946 is more than 11025). Euler's totient φ(11025) = 5040 numbers up to 11025 share no factor with it.
- 4
The digits of 11025 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 161 steps to reach 1.
LaTeX source of the formulas on this page
\[ 11025 = 3^{2} \times 5^{2} \times 7^{2} \]11025 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 27 |
| Sum of divisors | 22971 |
| Euler totient φ(n) | 5040 |
| Square | 121550625 |
| Cube | 1340095640625 |
| Square root | 105 |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 161 |
| Scientific notation | 1.1025 × |
| Perfect power |
11025 in other forms
| Form | Value |
|---|---|
| In words | eleven thousand and twenty-five |
| Binary (base 2) | 10101100010001 |
| Octal (base 8) | 25421 |
| Hexadecimal (base 16) | 2B11 |
| Base 3 | 120010100 |
| As time | 11025 seconds = 3 h 3 min 45 s |
Is 11025 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 (11025 ÷ 3 = 3675) | 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 (11025 ÷ 5 = 2205) | 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 | Yes (11025 ÷ 7 = 1575) | 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 1) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (11025 ÷ 9 = 1225) | 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 11025 a prime number?
No. 11025 = × × , so it is divisible by 3.
What are the factors of 11025?
1, 3, 5, 7, 9, 15, 21, 25, 35, 45, 49, 63, 75, 105, 147, 175, 225, 245, 315, 441, 525, 735, 1225, 1575, 2205, 3675, 11025.
What is 11025 in binary?
10101100010001 (hexadecimal 2B11, octal 25421).
What is the square root of 11025?
105, because 105 × 105 = 11025.
Is 11025 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 11025?
11025 is a perfect square (105²); a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 9.