The number 13023
13023 is a composite number with 6 divisors. Its prime factorisation is × 1447. Divisors (6): 1, 3, 9, 1447, 4341, 13023.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 13023: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 9.
- 2
13023 is composite. Its prime factorisation is
- 3
The divisors add up to 18824; without 13023 itself that is 5801, so 13023 is deficient (5801 is less than 13023). Euler's totient φ(13023) = 8676 numbers up to 13023 share no factor with it.
- 4
The digits of 13023 add up to 9, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 76 steps to reach 1.
LaTeX source of the formulas on this page
\[ 13023 = 3^{2} \times 1447 \]13023 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 6 |
| Sum of divisors | 18824 |
| Euler totient φ(n) | 8676 |
| Square | 169598529 |
| Cube | 2208681643167 |
| Square root | 114.118360 (= 3√1447) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 76 |
| Scientific notation | 1.3023 × |
13023 in other forms
| Form | Value |
|---|---|
| In words | thirteen thousand and twenty-three |
| Binary (base 2) | 11001011011111 |
| Octal (base 8) | 31337 |
| Hexadecimal (base 16) | 32DF |
| Base 3 | 122212100 |
| As time | 13023 seconds = 3 h 37 min 3 s |
Is 13023 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 (13023 ÷ 3 = 4341) | 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 3) | 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 | Yes (13023 ÷ 9 = 1447) | 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 10) | 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 13023 a prime number?
No. 13023 = × 1447, so it is divisible by 3.
What are the factors of 13023?
1, 3, 9, 1447, 4341, 13023.
What is 13023 in binary?
11001011011111 (hexadecimal 32DF, octal 31337).
What is the square root of 13023?
About 114.1184, exactly 3√1447.
Is 13023 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 13023?
13023 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 9.