The number 10004
10004 is a composite number with 12 divisors. Its prime factorisation is × 41 × 61. Divisors (12): 1, 2, 4, 41, 61, 82, 122, 164, 244, 2501, 5002, 10004.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
10004 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
10004 is composite. Its prime factorisation is
- 3
The divisors add up to 18228; without 10004 itself that is 8224, so 10004 is deficient (8224 is less than 10004). Euler's totient φ(10004) = 4800 numbers up to 10004 share no factor with it.
- 4
The digits of 10004 add up to 5, and repeating that until one digit is left gives the digital root 5. The Collatz sequence (halve if even, else 3n+1) takes 29 steps to reach 1.
LaTeX source of the formulas on this page
\[ 10004 = 2^{2} \times 41 \times 61 \]10004 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 18228 |
| Euler totient φ(n) | 4800 |
| Square | 100080016 |
| Cube | 1001200480064 |
| Square root | 100.019998 (= 2√2501) |
| Digit sum / digital root | 5 / 5 |
| Collatz steps to 1 | 29 |
| Scientific notation | 1.0004 × |
10004 in other forms
| Form | Value |
|---|---|
| In words | ten thousand and four |
| Binary (base 2) | 10011100010100 |
| Octal (base 8) | 23424 |
| Hexadecimal (base 16) | 2714 |
| Base 3 | 111201112 |
| As time | 10004 seconds = 2 h 46 min 44 s |
Is 10004 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (10004 ÷ 2 = 5002) | 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 (10004 ÷ 4 = 2501) | 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 | No (remainder 2) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 1) | 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 5) | 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 5) | 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 10004 a prime number?
No. 10004 = × 41 × 61, so it is divisible by 2.
What are the factors of 10004?
1, 2, 4, 41, 61, 82, 122, 164, 244, 2501, 5002, 10004.
What is 10004 in binary?
10011100010100 (hexadecimal 2714, octal 23424).
What is the square root of 10004?
About 100.0200, exactly 2√2501.
Is 10004 divisible by 3?
No. Its digits add up to 5, which is not a multiple of 3.
What is special about the number 10004?
It is a composite number with 12 divisors.