The number 10084
10084 is a composite number with 6 divisors. Its prime factorisation is × 2521. Divisors (6): 1, 2, 4, 2521, 5042, 10084.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
10084 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
10084 is composite. Its prime factorisation is
- 3
The divisors add up to 17654; without 10084 itself that is 7570, so 10084 is deficient (7570 is less than 10084). Euler's totient φ(10084) = 5040 numbers up to 10084 share no factor with it.
- 4
The digits of 10084 add up to 13, and repeating that until one digit is left gives the digital root 4. The Collatz sequence (halve if even, else 3n+1) takes 42 steps to reach 1.
LaTeX source of the formulas on this page
\[ 10084 = 2^{2} \times 2521 \]10084 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 6 |
| Sum of divisors | 17654 |
| Euler totient φ(n) | 5040 |
| Square | 101687056 |
| Cube | 1025412272704 |
| Square root | 100.419122 (= 2√2521) |
| Digit sum / digital root | 13 / 4 |
| Collatz steps to 1 | 42 |
| Scientific notation | 1.0084 × |
10084 in other forms
| Form | Value |
|---|---|
| In words | ten thousand and eighty-four |
| Binary (base 2) | 10011101100100 |
| Octal (base 8) | 23544 |
| Hexadecimal (base 16) | 2764 |
| Base 3 | 111211111 |
| As time | 10084 seconds = 2 h 48 min 4 s |
Is 10084 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (10084 ÷ 2 = 5042) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 1) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (10084 ÷ 4 = 2521) | 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 4) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 4) | 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 4) | 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 8) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 4) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 10084 a prime number?
No. 10084 = × 2521, so it is divisible by 2.
What are the factors of 10084?
1, 2, 4, 2521, 5042, 10084.
What is 10084 in binary?
10011101100100 (hexadecimal 2764, octal 23544).
What is the square root of 10084?
About 100.4191, exactly 2√2521.
Is 10084 divisible by 3?
No. Its digits add up to 13, which is not a multiple of 3.
What is special about the number 10084?
It is a composite number with 6 divisors.