The number 8000
8000 is a perfect cube (). Its prime factorisation is × . Divisors (28): 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 125 … 8000.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 8000: a perfect cube (); a Harshad number: divisible by its digit sum 8.
- 2
8000 is composite. Its prime factorisation is
- 3
The divisors add up to 19812; without 8000 itself that is 11812, so 8000 is abundant (11812 is more than 8000). Euler's totient φ(8000) = 3200 numbers up to 8000 share no factor with it.
- 4
The digits of 8000 add up to 8, and repeating that until one digit is left gives the digital root 8. The Collatz sequence (halve if even, else 3n+1) takes 114 steps to reach 1.
LaTeX source of the formulas on this page
\[ 8000 = 2^{6} \times 5^{3} \]8000 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 28 |
| Sum of divisors | 19812 |
| Euler totient φ(n) | 3200 |
| Square | 64000000 |
| Cube | 512000000000 |
| Square root | 89.442719 (= 40√5) |
| Digit sum / digital root | 8 / 8 |
| Collatz steps to 1 | 114 |
| Scientific notation | 8 × |
| Perfect power |
8000 in other forms
| Form | Value |
|---|---|
| In words | eight thousand |
| Binary (base 2) | 1111101000000 |
| Octal (base 8) | 17500 |
| Hexadecimal (base 16) | 1F40 |
| Base 3 | 101222022 |
| As time | 8000 seconds = 2 h 13 min 20 s |
Is 8000 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (8000 ÷ 2 = 4000) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 2) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (8000 ÷ 4 = 2000) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (8000 ÷ 5 = 1600) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 2) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 6) | 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 (8000 ÷ 8 = 1000) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 8) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (8000 ÷ 10 = 800) | 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 8) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 8000 a prime number?
No. 8000 = × , so it is divisible by 2.
What are the factors of 8000?
1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 125, 160, 200, 250, 320, 400, 500, 800, 1000, 1600, 2000, 4000, 8000.
What is 8000 in binary?
1111101000000 (hexadecimal 1F40, octal 17500).
What is the square root of 8000?
About 89.4427, exactly 40√5.
Is 8000 divisible by 3?
No. Its digits add up to 8, which is not a multiple of 3.
What is special about the number 8000?
8000 is a perfect cube (); a Harshad number: divisible by its digit sum 8.