The number 10011
10011 is a triangular number: 1 + 2 + … + 141 = 10011. Its prime factorisation is 3 × 47 × 71. Divisors (8): 1, 3, 47, 71, 141, 213, 3337, 10011.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 10011: a triangular number: 1 + 2 + … + 141 = 10011; a Harshad number: divisible by its digit sum 3.
- 2
10011 is composite. Its prime factorisation is
- 3
The divisors add up to 13824; without 10011 itself that is 3813, so 10011 is deficient (3813 is less than 10011). Euler's totient φ(10011) = 6440 numbers up to 10011 share no factor with it.
- 4
The digits of 10011 add up to 3, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 210 steps to reach 1.
LaTeX source of the formulas on this page
\[ 10011 = 3 \times 47 \times 71 \]
10011 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 8 |
| Sum of divisors | 13824 |
| Euler totient φ(n) | 6440 |
| Square | 100220121 |
| Cube | 1003303631331 |
| Square root | 100.054985 |
| Digit sum / digital root | 3 / 3 |
| Collatz steps to 1 | 210 |
| Scientific notation | 1.0011 × |
10011 in other forms
| Form | Value |
|---|---|
| In words | ten thousand and eleven |
| Binary (base 2) | 10011100011011 |
| Octal (base 8) | 23433 |
| Hexadecimal (base 16) | 271B |
| Base 3 | 111201210 |
| As time | 10011 seconds = 2 h 46 min 51 s |
Is 10011 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 (10011 ÷ 3 = 3337) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 3) | 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 3) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 1) | 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 3) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 3) | 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 1) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 3) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 10011 a prime number?
No. 10011 = 3 × 47 × 71, so it is divisible by 3.
What are the factors of 10011?
1, 3, 47, 71, 141, 213, 3337, 10011.
What is 10011 in binary?
10011100011011 (hexadecimal 271B, octal 23433).
What is the square root of 10011?
About 100.0550.
Is 10011 divisible by 3?
Yes. Its digits add up to 3, a multiple of 3.
What is special about the number 10011?
10011 is a triangular number: 1 + 2 + … + 141 = 10011; a Harshad number: divisible by its digit sum 3.