The number 9000
9000 is a composite number with 48 divisors. Its prime factorisation is × × . Divisors (48): 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 25, 30 … 9000.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 9000: a Harshad number: divisible by its digit sum 9.
- 2
9000 is composite. Its prime factorisation is
- 3
The divisors add up to 30420; without 9000 itself that is 21420, so 9000 is abundant (21420 is more than 9000). Euler's totient φ(9000) = 2400 numbers up to 9000 share no factor with it.
- 4
The digits of 9000 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 47 steps to reach 1.
LaTeX source of the formulas on this page
\[ 9000 = 2^{3} \times 3^{2} \times 5^{3} \]9000 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 30420 |
| Euler totient φ(n) | 2400 |
| Square | 81000000 |
| Cube | 729000000000 |
| Square root | 94.868330 (= 30√10) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 47 |
| Scientific notation | 9 × |
9000 in other forms
| Form | Value |
|---|---|
| In words | nine thousand |
| Binary (base 2) | 10001100101000 |
| Octal (base 8) | 21450 |
| Hexadecimal (base 16) | 2328 |
| Base 3 | 110100100 |
| As time | 9000 seconds = 2 h 30 min 0 s |
Is 9000 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (9000 ÷ 2 = 4500) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (9000 ÷ 3 = 3000) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (9000 ÷ 4 = 2250) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (9000 ÷ 5 = 1800) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (9000 ÷ 6 = 1500) | 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 | Yes (9000 ÷ 8 = 1125) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (9000 ÷ 9 = 1000) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (9000 ÷ 10 = 900) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 2) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (9000 ÷ 12 = 750) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 9000 a prime number?
No. 9000 = × × , so it is divisible by 2.
What are the factors of 9000?
1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 25, 30, 36, 40, 45, 50, 60, 72, 75, 90, 100, 120, 125, 150, 180, 200, 225, 250, 300, 360, 375, 450, 500, 600, 750, 900, 1000, 1125, 1500, 1800, 2250, 3000, 4500, 9000.
What is 9000 in binary?
10001100101000 (hexadecimal 2328, octal 21450).
What is the square root of 9000?
About 94.8683, exactly 30√10.
Is 9000 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 9000?
9000 is a Harshad number: divisible by its digit sum 9.