The number 8004
8004 is a composite number with 24 divisors. Its prime factorisation is × 3 × 23 × 29. Divisors (24): 1, 2, 3, 4, 6, 12, 23, 29, 46, 58, 69, 87, 92, 116, 138, 174 … 8004.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 8004: a Harshad number: divisible by its digit sum 12.
- 2
8004 is composite. Its prime factorisation is
- 3
The divisors add up to 20160; without 8004 itself that is 12156, so 8004 is abundant (12156 is more than 8004). Euler's totient φ(8004) = 2464 numbers up to 8004 share no factor with it.
- 4
The digits of 8004 add up to 12, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 52 steps to reach 1.
LaTeX source of the formulas on this page
\[ 8004 = 2^{2} \times 3 \times 23 \times 29 \]8004 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 20160 |
| Euler totient φ(n) | 2464 |
| Square | 64064016 |
| Cube | 512768384064 |
| Square root | 89.465077 (= 2√2001) |
| Digit sum / digital root | 12 / 3 |
| Collatz steps to 1 | 52 |
| Scientific notation | 8.004 × |
8004 in other forms
| Form | Value |
|---|---|
| In words | eight thousand and four |
| Binary (base 2) | 1111101000100 |
| Octal (base 8) | 17504 |
| Hexadecimal (base 16) | 1F44 |
| Base 3 | 101222110 |
| As time | 8004 seconds = 2 h 13 min 24 s |
Is 8004 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (8004 ÷ 2 = 4002) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (8004 ÷ 3 = 2668) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (8004 ÷ 4 = 2001) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 4) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (8004 ÷ 6 = 1334) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 3) | 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 4) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 3) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 4) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 7) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (8004 ÷ 12 = 667) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 8004 a prime number?
No. 8004 = × 3 × 23 × 29, so it is divisible by 2.
What are the factors of 8004?
1, 2, 3, 4, 6, 12, 23, 29, 46, 58, 69, 87, 92, 116, 138, 174, 276, 348, 667, 1334, 2001, 2668, 4002, 8004.
What is 8004 in binary?
1111101000100 (hexadecimal 1F44, octal 17504).
What is the square root of 8004?
About 89.4651, exactly 2√2001.
Is 8004 divisible by 3?
Yes. Its digits add up to 12, a multiple of 3.
What is special about the number 8004?
8004 is a Harshad number: divisible by its digit sum 12.