The number 13832
13832 is a taxicab number: it is the sum of two cubes in 2 ways (2³ + 24³ and 18³ + 20³). Its prime factorisation is × 7 × 13 × 19. Divisors (32): 1, 2, 4, 7, 8, 13, 14, 19, 26, 28, 38, 52, 56, 76, 91, 104 … 13832.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 13832: a taxicab number: it is the sum of two cubes in 2 ways (2³ + 24³ and 18³ + 20³).
- 2
13832 is composite. Its prime factorisation is
- 3
The divisors add up to 33600; without 13832 itself that is 19768, so 13832 is abundant (19768 is more than 13832). Euler's totient φ(13832) = 5184 numbers up to 13832 share no factor with it.
- 4
The digits of 13832 add up to 17, and repeating that until one digit is left gives the digital root 8. The Collatz sequence (halve if even, else 3n+1) takes 107 steps to reach 1.
LaTeX source of the formulas on this page
\[ 13832 = 2^{3} \times 7 \times 13 \times 19 \]13832 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 32 |
| Sum of divisors | 33600 |
| Euler totient φ(n) | 5184 |
| Square | 191324224 |
| Cube | 2646396666368 |
| Square root | 117.609523 (= 2√3458) |
| Digit sum / digital root | 17 / 8 |
| Collatz steps to 1 | 107 |
| Scientific notation | 1.3832 × |
13832 in other forms
| Form | Value |
|---|---|
| In words | thirteen thousand eight hundred and thirty-two |
| Binary (base 2) | 11011000001000 |
| Octal (base 8) | 33010 |
| Hexadecimal (base 16) | 3608 |
| Base 3 | 200222022 |
| As time | 13832 seconds = 3 h 50 min 32 s |
Is 13832 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (13832 ÷ 2 = 6916) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 2) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (13832 ÷ 4 = 3458) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 2) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 2) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (13832 ÷ 7 = 1976) | 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 (13832 ÷ 8 = 1729) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 8) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 2) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 5) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 8) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 13832 a prime number?
No. 13832 = × 7 × 13 × 19, so it is divisible by 2.
What are the factors of 13832?
1, 2, 4, 7, 8, 13, 14, 19, 26, 28, 38, 52, 56, 76, 91, 104, 133, 152, 182, 247, 266, 364, 494, 532, 728, 988, 1064, 1729, 1976, 3458, 6916, 13832.
What is 13832 in binary?
11011000001000 (hexadecimal 3608, octal 33010).
What is the square root of 13832?
About 117.6095, exactly 2√3458.
Is 13832 divisible by 3?
No. Its digits add up to 17, which is not a multiple of 3.
What is special about the number 13832?
13832 is a taxicab number: it is the sum of two cubes in 2 ways (2³ + 24³ and 18³ + 20³).