The number 8007
8007 is a composite number with 8 divisors. Its prime factorisation is 3 × 17 × 157. Divisors (8): 1, 3, 17, 51, 157, 471, 2669, 8007.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
8007 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
8007 is composite. Its prime factorisation is
- 3
The divisors add up to 11376; without 8007 itself that is 3369, so 8007 is deficient (3369 is less than 8007). Euler's totient φ(8007) = 4992 numbers up to 8007 share no factor with it.
- 4
The digits of 8007 add up to 15, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 44 steps to reach 1.
LaTeX source of the formulas on this page
\[ 8007 = 3 \times 17 \times 157 \]
8007 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 8 |
| Sum of divisors | 11376 |
| Euler totient φ(n) | 4992 |
| Square | 64112049 |
| Cube | 513345176343 |
| Square root | 89.481842 |
| Digit sum / digital root | 15 / 6 |
| Collatz steps to 1 | 44 |
| Scientific notation | 8.007 × |
8007 in other forms
| Form | Value |
|---|---|
| In words | eight thousand and seven |
| Binary (base 2) | 1111101000111 |
| Octal (base 8) | 17507 |
| Hexadecimal (base 16) | 1F47 |
| Base 3 | 101222120 |
| As time | 8007 seconds = 2 h 13 min 27 s |
Is 8007 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 (8007 ÷ 3 = 2669) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 3) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 2) | 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 | 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 | No (remainder 7) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 6) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 7) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 10) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 3) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 8007 a prime number?
No. 8007 = 3 × 17 × 157, so it is divisible by 3.
What are the factors of 8007?
1, 3, 17, 51, 157, 471, 2669, 8007.
What is 8007 in binary?
1111101000111 (hexadecimal 1F47, octal 17507).
What is the square root of 8007?
About 89.4818.
Is 8007 divisible by 3?
Yes. Its digits add up to 15, a multiple of 3.
What is special about the number 8007?
It is a composite number with 8 divisors.