The number 13024
13024 is a composite number with 24 divisors. Its prime factorisation is × 11 × 37. Divisors (24): 1, 2, 4, 8, 11, 16, 22, 32, 37, 44, 74, 88, 148, 176, 296, 352 … 13024.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
13024 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
13024 is composite. Its prime factorisation is
- 3
The divisors add up to 28728; without 13024 itself that is 15704, so 13024 is abundant (15704 is more than 13024). Euler's totient φ(13024) = 5760 numbers up to 13024 share no factor with it.
- 4
The digits of 13024 add up to 10, and repeating that until one digit is left gives the digital root 1. The Collatz sequence (halve if even, else 3n+1) takes 45 steps to reach 1.
LaTeX source of the formulas on this page
\[ 13024 = 2^{5} \times 11 \times 37 \]13024 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 28728 |
| Euler totient φ(n) | 5760 |
| Square | 169624576 |
| Cube | 2209190477824 |
| Square root | 114.122741 (= 4√814) |
| Digit sum / digital root | 10 / 1 |
| Collatz steps to 1 | 45 |
| Scientific notation | 1.3024 × |
13024 in other forms
| Form | Value |
|---|---|
| In words | thirteen thousand and twenty-four |
| Binary (base 2) | 11001011100000 |
| Octal (base 8) | 31340 |
| Hexadecimal (base 16) | 32E0 |
| Base 3 | 122212101 |
| As time | 13024 seconds = 3 h 37 min 4 s |
Is 13024 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (13024 ÷ 2 = 6512) | 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 (13024 ÷ 4 = 3256) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 4) | 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 (13024 ÷ 8 = 1628) | 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 | No (remainder 4) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (13024 ÷ 11 = 1184) | 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 13024 a prime number?
No. 13024 = × 11 × 37, so it is divisible by 2.
What are the factors of 13024?
1, 2, 4, 8, 11, 16, 22, 32, 37, 44, 74, 88, 148, 176, 296, 352, 407, 592, 814, 1184, 1628, 3256, 6512, 13024.
What is 13024 in binary?
11001011100000 (hexadecimal 32E0, octal 31340).
What is the square root of 13024?
About 114.1227, exactly 4√814.
Is 13024 divisible by 3?
No. Its digits add up to 10, which is not a multiple of 3.
What is special about the number 13024?
It is a composite number with 24 divisors.