The number 10008
10008 is a composite number with 24 divisors. Its prime factorisation is × × 139. Divisors (24): 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72, 139, 278, 417, 556 … 10008.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 10008: a Harshad number: divisible by its digit sum 9.
- 2
10008 is composite. Its prime factorisation is
- 3
The divisors add up to 27300; without 10008 itself that is 17292, so 10008 is abundant (17292 is more than 10008). Euler's totient φ(10008) = 3312 numbers up to 10008 share no factor with it.
- 4
The digits of 10008 add up to 9, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 29 steps to reach 1.
LaTeX source of the formulas on this page
\[ 10008 = 2^{3} \times 3^{2} \times 139 \]10008 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 27300 |
| Euler totient φ(n) | 3312 |
| Square | 100160064 |
| Cube | 1002401920512 |
| Square root | 100.039992 (= 6√278) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 29 |
| Scientific notation | 1.0008 × |
10008 in other forms
| Form | Value |
|---|---|
| In words | ten thousand and eight |
| Binary (base 2) | 10011100011000 |
| Octal (base 8) | 23430 |
| Hexadecimal (base 16) | 2718 |
| Base 3 | 111201200 |
| As time | 10008 seconds = 2 h 46 min 48 s |
Is 10008 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (10008 ÷ 2 = 5004) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (10008 ÷ 3 = 3336) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (10008 ÷ 4 = 2502) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 3) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (10008 ÷ 6 = 1668) | 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 | Yes (10008 ÷ 8 = 1251) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (10008 ÷ 9 = 1112) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 8) | 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 | Yes (10008 ÷ 12 = 834) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 10008 a prime number?
No. 10008 = × × 139, so it is divisible by 2.
What are the factors of 10008?
1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72, 139, 278, 417, 556, 834, 1112, 1251, 1668, 2502, 3336, 5004, 10008.
What is 10008 in binary?
10011100011000 (hexadecimal 2718, octal 23430).
What is the square root of 10008?
About 100.0400, exactly 6√278.
Is 10008 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 10008?
10008 is a Harshad number: divisible by its digit sum 9.