The number 13830
13830 is a composite number with 16 divisors. Its prime factorisation is 2 × 3 × 5 × 461. Divisors (16): 1, 2, 3, 5, 6, 10, 15, 30, 461, 922, 1383, 2305, 2766, 4610, 6915, 13830.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 13830: a Harshad number: divisible by its digit sum 15.
- 2
13830 is composite. Its prime factorisation is
- 3
The divisors add up to 33264; without 13830 itself that is 19434, so 13830 is abundant (19434 is more than 13830). Euler's totient φ(13830) = 3680 numbers up to 13830 share no factor with it.
- 4
The digits of 13830 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 45 steps to reach 1.
LaTeX source of the formulas on this page
\[ 13830 = 2 \times 3 \times 5 \times 461 \]
13830 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 16 |
| Sum of divisors | 33264 |
| Euler totient φ(n) | 3680 |
| Square | 191268900 |
| Cube | 2645248887000 |
| Square root | 117.601020 |
| Digit sum / digital root | 15 / 6 |
| Collatz steps to 1 | 45 |
| Scientific notation | 1.383 × |
13830 in other forms
| Form | Value |
|---|---|
| In words | thirteen thousand eight hundred and thirty |
| Binary (base 2) | 11011000000110 |
| Octal (base 8) | 33006 |
| Hexadecimal (base 16) | 3606 |
| Base 3 | 200222020 |
| As time | 13830 seconds = 3 h 50 min 30 s |
Is 13830 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (13830 ÷ 2 = 6915) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (13830 ÷ 3 = 4610) | 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 | Yes (13830 ÷ 5 = 2766) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (13830 ÷ 6 = 2305) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 5) | 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 | Yes (13830 ÷ 10 = 1383) | 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 13830 a prime number?
No. 13830 = 2 × 3 × 5 × 461, so it is divisible by 2.
What are the factors of 13830?
1, 2, 3, 5, 6, 10, 15, 30, 461, 922, 1383, 2305, 2766, 4610, 6915, 13830.
What is 13830 in binary?
11011000000110 (hexadecimal 3606, octal 33006).
What is the square root of 13830?
About 117.6010.
Is 13830 divisible by 3?
Yes. Its digits add up to 15, a multiple of 3.
What is special about the number 13830?
13830 is a Harshad number: divisible by its digit sum 15.