The number 10001
10001 is a palindrome: it reads 10001 backwards too. Its prime factorisation is 73 × 137. Divisors (4): 1, 73, 137, 10001.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 10001: a palindrome: it reads 10001 backwards too; a semiprime: 73 × 137, the product of two primes.
- 2
10001 is composite. Its prime factorisation is
- 3
The divisors add up to 10212; without 10001 itself that is 211, so 10001 is deficient (211 is less than 10001). Euler's totient φ(10001) = 9792 numbers up to 10001 share no factor with it.
- 4
The digits of 10001 add up to 2, and repeating that until one digit is left gives the digital root 2. The Collatz sequence (halve if even, else 3n+1) takes 179 steps to reach 1.
LaTeX source of the formulas on this page
\[ 10001 = 73 \times 137 \]
10001 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 4 |
| Sum of divisors | 10212 |
| Euler totient φ(n) | 9792 |
| Square | 100020001 |
| Cube | 1000300030001 |
| Square root | 100.005000 |
| Digit sum / digital root | 2 / 2 |
| Collatz steps to 1 | 179 |
| Scientific notation | 1.0001 × |
10001 in other forms
| Form | Value |
|---|---|
| In words | ten thousand and one |
| Binary (base 2) | 10011100010001 |
| Octal (base 8) | 23421 |
| Hexadecimal (base 16) | 2711 |
| Base 3 | 111201102 |
| As time | 10001 seconds = 2 h 46 min 41 s |
Is 10001 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 | No (remainder 2) | 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 | No (remainder 1) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 5) | 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 | No (remainder 1) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 2) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 1) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 2) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 5) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 10001 a prime number?
No. 10001 = 73 × 137, so it is divisible by 73.
What are the factors of 10001?
1, 73, 137, 10001.
What is 10001 in binary?
10011100010001 (hexadecimal 2711, octal 23421).
What is the square root of 10001?
About 100.0050.
Is 10001 divisible by 3?
No. Its digits add up to 2, which is not a multiple of 3.
What is special about the number 10001?
10001 is a palindrome: it reads 10001 backwards too; a semiprime: 73 × 137, the product of two primes.