The number 13038
13038 is a composite number with 16 divisors. Its prime factorisation is 2 × 3 × 41 × 53. Divisors (16): 1, 2, 3, 6, 41, 53, 82, 106, 123, 159, 246, 318, 2173, 4346, 6519, 13038.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
13038 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
13038 is composite. Its prime factorisation is
- 3
The divisors add up to 27216; without 13038 itself that is 14178, so 13038 is abundant (14178 is more than 13038). Euler's totient φ(13038) = 4160 numbers up to 13038 share no factor with it.
- 4
The digits of 13038 add up to 15, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 50 steps to reach 1.
LaTeX source of the formulas on this page
\[ 13038 = 2 \times 3 \times 41 \times 53 \]
13038 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 16 |
| Sum of divisors | 27216 |
| Euler totient φ(n) | 4160 |
| Square | 169989444 |
| Cube | 2216322370872 |
| Square root | 114.184062 |
| Digit sum / digital root | 15 / 6 |
| Collatz steps to 1 | 50 |
| Scientific notation | 1.3038 × |
13038 in other forms
| Form | Value |
|---|---|
| In words | thirteen thousand and thirty-eight |
| Binary (base 2) | 11001011101110 |
| Octal (base 8) | 31356 |
| Hexadecimal (base 16) | 32EE |
| Base 3 | 122212220 |
| As time | 13038 seconds = 3 h 37 min 18 s |
Is 13038 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (13038 ÷ 2 = 6519) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (13038 ÷ 3 = 4346) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 2) | 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 | Yes (13038 ÷ 6 = 2173) | 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 | No (remainder 6) | 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 8) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 3) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 6) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 13038 a prime number?
No. 13038 = 2 × 3 × 41 × 53, so it is divisible by 2.
What are the factors of 13038?
1, 2, 3, 6, 41, 53, 82, 106, 123, 159, 246, 318, 2173, 4346, 6519, 13038.
What is 13038 in binary?
11001011101110 (hexadecimal 32EE, octal 31356).
What is the square root of 13038?
About 114.1841.
Is 13038 divisible by 3?
Yes. Its digits add up to 15, a multiple of 3.
What is special about the number 13038?
It is a composite number with 16 divisors.