The number 10023
10023 is a composite number with 8 divisors. Its prime factorisation is 3 × 13 × 257. Divisors (8): 1, 3, 13, 39, 257, 771, 3341, 10023.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
10023 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
10023 is composite. Its prime factorisation is
- 3
The divisors add up to 14448; without 10023 itself that is 4425, so 10023 is deficient (4425 is less than 10023). Euler's totient φ(10023) = 6144 numbers up to 10023 share no factor with it.
- 4
The digits of 10023 add up to 6, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 65 steps to reach 1.
LaTeX source of the formulas on this page
\[ 10023 = 3 \times 13 \times 257 \]
10023 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 8 |
| Sum of divisors | 14448 |
| Euler totient φ(n) | 6144 |
| Square | 100460529 |
| Cube | 1006915882167 |
| Square root | 100.114934 |
| Digit sum / digital root | 6 / 6 |
| Collatz steps to 1 | 65 |
| Scientific notation | 1.0023 × |
10023 in other forms
| Form | Value |
|---|---|
| In words | ten thousand and twenty-three |
| Binary (base 2) | 10011100100111 |
| Octal (base 8) | 23447 |
| Hexadecimal (base 16) | 2727 |
| Base 3 | 111202020 |
| As time | 10023 seconds = 2 h 47 min 3 s |
Is 10023 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 (10023 ÷ 3 = 3341) | 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 3) | 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 6) | 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 7) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 6) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 3) | 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 3) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 10023 a prime number?
No. 10023 = 3 × 13 × 257, so it is divisible by 3.
What are the factors of 10023?
1, 3, 13, 39, 257, 771, 3341, 10023.
What is 10023 in binary?
10011100100111 (hexadecimal 2727, octal 23447).
What is the square root of 10023?
About 100.1149.
Is 10023 divisible by 3?
Yes. Its digits add up to 6, a multiple of 3.
What is special about the number 10023?
It is a composite number with 8 divisors.