The number 22500
22500 is a perfect square (150²). Its prime factorisation is × × . Divisors (45): 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45 … 22500.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 22500: a perfect square (150²); a Harshad number: divisible by its digit sum 9.
- 2
22500 is composite. Its prime factorisation is
- 3
The divisors add up to 71071; without 22500 itself that is 48571, so 22500 is abundant (48571 is more than 22500). Euler's totient φ(22500) = 6000 numbers up to 22500 share no factor with it.
- 4
The digits of 22500 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 162 steps to reach 1.
LaTeX source of the formulas on this page
\[ 22500 = 2^{2} \times 3^{2} \times 5^{4} \]22500 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 45 |
| Sum of divisors | 71071 |
| Euler totient φ(n) | 6000 |
| Square | 506250000 |
| Cube | 11390625000000 |
| Square root | 150 |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 162 |
| Scientific notation | 2.25 × |
| Perfect power |
22500 in other forms
| Form | Value |
|---|---|
| In words | twenty-two thousand five hundred |
| Binary (base 2) | 101011111100100 |
| Octal (base 8) | 53744 |
| Hexadecimal (base 16) | 57E4 |
| Base 3 | 1010212100 |
| As time | 22500 seconds = 6 h 15 min 0 s |
Is 22500 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (22500 ÷ 2 = 11250) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (22500 ÷ 3 = 7500) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (22500 ÷ 4 = 5625) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (22500 ÷ 5 = 4500) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (22500 ÷ 6 = 3750) | 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 4) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (22500 ÷ 9 = 2500) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (22500 ÷ 10 = 2250) | 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 | Yes (22500 ÷ 12 = 1875) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 22500 a prime number?
No. 22500 = × × , so it is divisible by 2.
What are the factors of 22500?
1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 50, 60, 75, 90, 100, 125, 150, 180, 225, 250, 300, 375, 450, 500, 625, 750, 900, 1125, 1250, 1500, 1875, 2250, 2500, 3750, 4500, 5625, 7500, 11250, 22500.
What is 22500 in binary?
101011111100100 (hexadecimal 57E4, octal 53744).
What is the square root of 22500?
150, because 150 × 150 = 22500.
Is 22500 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 22500?
22500 is a perfect square (150²); a Harshad number: divisible by its digit sum 9.