The number 27225
27225 is a perfect square (165²). Its prime factorisation is × × . Divisors (27): 1, 3, 5, 9, 11, 15, 25, 33, 45, 55, 75, 99, 121, 165, 225, 275 … 27225.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 27225: a perfect square (165²); a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
27225 is composite. Its prime factorisation is
- 3
The divisors add up to 53599; without 27225 itself that is 26374, so 27225 is deficient (26374 is less than 27225). Euler's totient φ(27225) = 13200 numbers up to 27225 share no factor with it.
- 4
The digits of 27225 add up to 18, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 90 steps to reach 1.
LaTeX source of the formulas on this page
\[ 27225 = 3^{2} \times 5^{2} \times 11^{2} \]27225 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 27 |
| Sum of divisors | 53599 |
| Euler totient φ(n) | 13200 |
| Square | 741200625 |
| Cube | 20179187015625 |
| Square root | 165 |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 90 |
| Scientific notation | 2.7225 × |
| Perfect power |
27225 in other forms
| Form | Value |
|---|---|
| In words | twenty-seven thousand two hundred and twenty-five |
| Binary (base 2) | 110101001011001 |
| Octal (base 8) | 65131 |
| Hexadecimal (base 16) | 6A59 |
| Base 3 | 1101100100 |
| As time | 27225 seconds = 7 h 33 min 45 s |
Is 27225 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 (27225 ÷ 3 = 9075) | 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 (27225 ÷ 5 = 5445) | 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 2) | 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 (27225 ÷ 9 = 3025) | 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 | Yes (27225 ÷ 11 = 2475) | 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 27225 a prime number?
No. 27225 = × × , so it is divisible by 3.
What are the factors of 27225?
1, 3, 5, 9, 11, 15, 25, 33, 45, 55, 75, 99, 121, 165, 225, 275, 363, 495, 605, 825, 1089, 1815, 2475, 3025, 5445, 9075, 27225.
What is 27225 in binary?
110101001011001 (hexadecimal 6A59, octal 65131).
What is the square root of 27225?
165, because 165 × 165 = 27225.
Is 27225 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 27225?
27225 is a perfect square (165²); a happy number: repeatedly adding the squares of its digits reaches 1.