The number 8006
8006 is a composite number with 4 divisors. Its prime factorisation is 2 × 4003. Divisors (4): 1, 2, 4003, 8006.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 8006: a happy number: repeatedly adding the squares of its digits reaches 1; a semiprime: 2 × 4003, the product of two primes.
- 2
8006 is composite. Its prime factorisation is
- 3
The divisors add up to 12012; without 8006 itself that is 4006, so 8006 is deficient (4006 is less than 8006). Euler's totient φ(8006) = 4002 numbers up to 8006 share no factor with it.
- 4
The digits of 8006 add up to 14, and repeating that until one digit is left gives the digital root 5. The Collatz sequence (halve if even, else 3n+1) takes 52 steps to reach 1.
LaTeX source of the formulas on this page
\[ 8006 = 2 \times 4003 \]
8006 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 4 |
| Sum of divisors | 12012 |
| Euler totient φ(n) | 4002 |
| Square | 64096036 |
| Cube | 513152864216 |
| Square root | 89.476254 |
| Digit sum / digital root | 14 / 5 |
| Collatz steps to 1 | 52 |
| Scientific notation | 8.006 × |
8006 in other forms
| Form | Value |
|---|---|
| In words | eight thousand and six |
| Binary (base 2) | 1111101000110 |
| Octal (base 8) | 17506 |
| Hexadecimal (base 16) | 1F46 |
| Base 3 | 101222112 |
| As time | 8006 seconds = 2 h 13 min 26 s |
Is 8006 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (8006 ÷ 2 = 4003) | 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 | No (remainder 2) | 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 2) | 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 | No (remainder 6) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 5) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 6) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 9) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 2) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 8006 a prime number?
No. 8006 = 2 × 4003, so it is divisible by 2.
What are the factors of 8006?
1, 2, 4003, 8006.
What is 8006 in binary?
1111101000110 (hexadecimal 1F46, octal 17506).
What is the square root of 8006?
About 89.4763.
Is 8006 divisible by 3?
No. Its digits add up to 14, which is not a multiple of 3.
What is special about the number 8006?
8006 is a happy number: repeatedly adding the squares of its digits reaches 1; a semiprime: 2 × 4003, the product of two primes.