The number 8001
8001 is a triangular number: 1 + 2 + … + 126 = 8001. Its prime factorisation is × 7 × 127. Divisors (12): 1, 3, 7, 9, 21, 63, 127, 381, 889, 1143, 2667, 8001.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 8001: a triangular number: 1 + 2 + … + 126 = 8001; a Harshad number: divisible by its digit sum 9.
- 2
8001 is composite. Its prime factorisation is
- 3
The divisors add up to 13312; without 8001 itself that is 5311, so 8001 is deficient (5311 is less than 8001). Euler's totient φ(8001) = 4536 numbers up to 8001 share no factor with it.
- 4
The digits of 8001 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
\[ 8001 = 3^{2} \times 7 \times 127 \]8001 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 13312 |
| Euler totient φ(n) | 4536 |
| Square | 64016001 |
| Cube | 512192024001 |
| Square root | 89.448309 (= 3√889) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 52 |
| Scientific notation | 8.001 × |
8001 in other forms
| Form | Value |
|---|---|
| In words | eight thousand and one |
| Binary (base 2) | 1111101000001 |
| Octal (base 8) | 17501 |
| Hexadecimal (base 16) | 1F41 |
| Base 3 | 101222100 |
| As time | 8001 seconds = 2 h 13 min 21 s |
Is 8001 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 (8001 ÷ 3 = 2667) | 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 | No (remainder 1) | 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 | Yes (8001 ÷ 7 = 1143) | 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 (8001 ÷ 9 = 889) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 1) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 4) | 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 8001 a prime number?
No. 8001 = × 7 × 127, so it is divisible by 3.
What are the factors of 8001?
1, 3, 7, 9, 21, 63, 127, 381, 889, 1143, 2667, 8001.
What is 8001 in binary?
1111101000001 (hexadecimal 1F41, octal 17501).
What is the square root of 8001?
About 89.4483, exactly 3√889.
Is 8001 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 8001?
8001 is a triangular number: 1 + 2 + … + 126 = 8001; a Harshad number: divisible by its digit sum 9.