The number 10000
10000 is a perfect power () and a perfect square (100²). Its prime factorisation is × . Divisors (25): 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 125, 200, 250 … 10000.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 10000: a perfect power (); a perfect square (100²); a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 1.
- 2
10000 is composite. Its prime factorisation is
- 3
The divisors add up to 24211; without 10000 itself that is 14211, so 10000 is abundant (14211 is more than 10000). Euler's totient φ(10000) = 4000 numbers up to 10000 share no factor with it.
- 4
The digits of 10000 add up to 1, and repeating that until one digit is left gives the digital root 1. The Collatz sequence (halve if even, else 3n+1) takes 29 steps to reach 1.
LaTeX source of the formulas on this page
\[ 10000 = 2^{4} \times 5^{4} \]10000 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 25 |
| Sum of divisors | 24211 |
| Euler totient φ(n) | 4000 |
| Square | 100000000 |
| Cube | 1000000000000 |
| Square root | 100 |
| Digit sum / digital root | 1 / 1 |
| Collatz steps to 1 | 29 |
| Scientific notation | 1 × |
| Perfect power |
10000 in other forms
| Form | Value |
|---|---|
| In words | ten thousand |
| Binary (base 2) | 10011100010000 |
| Octal (base 8) | 23420 |
| Hexadecimal (base 16) | 2710 |
| Base 3 | 111201101 |
| As time | 10000 seconds = 2 h 46 min 40 s |
Is 10000 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (10000 ÷ 2 = 5000) | 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 (10000 ÷ 4 = 2500) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (10000 ÷ 5 = 2000) | 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 | Yes (10000 ÷ 8 = 1250) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 1) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (10000 ÷ 10 = 1000) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 1) | 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 10000 a prime number?
No. 10000 = × , so it is divisible by 2.
What are the factors of 10000?
1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 125, 200, 250, 400, 500, 625, 1000, 1250, 2000, 2500, 5000, 10000.
What is 10000 in binary?
10011100010000 (hexadecimal 2710, octal 23420).
What is the square root of 10000?
100, because 100 × 100 = 10000.
Is 10000 divisible by 3?
No. Its digits add up to 1, which is not a multiple of 3.
What is special about the number 10000?
10000 is a perfect power (); a perfect square (100²); a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 1.