The number 10005
10005 is a composite number with 16 divisors. Its prime factorisation is 3 × 5 × 23 × 29. Divisors (16): 1, 3, 5, 15, 23, 29, 69, 87, 115, 145, 345, 435, 667, 2001, 3335, 10005.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
10005 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
10005 is composite. Its prime factorisation is
- 3
The divisors add up to 17280; without 10005 itself that is 7275, so 10005 is deficient (7275 is less than 10005). Euler's totient φ(10005) = 4928 numbers up to 10005 share no factor with it.
- 4
The digits of 10005 add up to 6, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 29 steps to reach 1.
LaTeX source of the formulas on this page
\[ 10005 = 3 \times 5 \times 23 \times 29 \]
10005 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 16 |
| Sum of divisors | 17280 |
| Euler totient φ(n) | 4928 |
| Square | 100100025 |
| Cube | 1001500750125 |
| Square root | 100.024997 |
| Digit sum / digital root | 6 / 6 |
| Collatz steps to 1 | 29 |
| Scientific notation | 1.0005 × |
10005 in other forms
| Form | Value |
|---|---|
| In words | ten thousand and five |
| Binary (base 2) | 10011100010101 |
| Octal (base 8) | 23425 |
| Hexadecimal (base 16) | 2715 |
| Base 3 | 111201120 |
| As time | 10005 seconds = 2 h 46 min 45 s |
Is 10005 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 (10005 ÷ 3 = 3335) | 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 | Yes (10005 ÷ 5 = 2001) | 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 2) | 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 5) | 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 5) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 6) | 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 10005 a prime number?
No. 10005 = 3 × 5 × 23 × 29, so it is divisible by 3.
What are the factors of 10005?
1, 3, 5, 15, 23, 29, 69, 87, 115, 145, 345, 435, 667, 2001, 3335, 10005.
What is 10005 in binary?
10011100010101 (hexadecimal 2715, octal 23425).
What is the square root of 10005?
About 100.0250.
Is 10005 divisible by 3?
Yes. Its digits add up to 6, a multiple of 3.
What is special about the number 10005?
It is a composite number with 16 divisors.