The number 225
225 is a perfect square (15²). Its prime factorisation is × . Divisors (9): 1, 3, 5, 9, 15, 25, 45, 75, 225.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 225: a perfect square (15²); a Harshad number: divisible by its digit sum 9.
- 2
225 is composite. Its prime factorisation is
- 3
The divisors add up to 403; without 225 itself that is 178, so 225 is deficient (178 is less than 225). Euler's totient φ(225) = 120 numbers up to 225 share no factor with it.
- 4
The digits of 225 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 52 steps to reach 1.
LaTeX source of the formulas on this page
\[ 225 = 3^{2} \times 5^{2} \]225 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 9 |
| Sum of divisors | 403 |
| Euler totient φ(n) | 120 |
| Square | 50625 |
| Cube | 11390625 |
| Square root | 15 |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 52 |
| Scientific notation | 2.25 × |
| Perfect power |
225 in other forms
| Form | Value |
|---|---|
| In words | two hundred and twenty-five |
| Roman numerals | CCXXV |
| Binary (base 2) | 11100001 |
| Octal (base 8) | 341 |
| Hexadecimal (base 16) | E1 |
| Base 3 | 22100 |
| As time | 225 seconds = 3 min 45 s |
Is 225 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 (225 ÷ 3 = 75) | 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 (225 ÷ 5 = 45) | 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 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 | No (remainder 1) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (225 ÷ 9 = 25) | 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 5) | 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 225 a prime number?
No. 225 = × , so it is divisible by 3.
What are the factors of 225?
1, 3, 5, 9, 15, 25, 45, 75, 225.
What is 225 in binary?
11100001 (hexadecimal E1, octal 341).
What is the square root of 225?
15, because 15 × 15 = 225.
What is 225 in Roman numerals?
CCXXV.
Is 225 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 225?
225 is a perfect square (15²); a Harshad number: divisible by its digit sum 9.