The number 13878
13878 is a composite number with 16 divisors. Its prime factorisation is 2 × × 257. Divisors (16): 1, 2, 3, 6, 9, 18, 27, 54, 257, 514, 771, 1542, 2313, 4626, 6939, 13878.
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How to work it out
- 1
What is special about 13878: a Harshad number: divisible by its digit sum 27.
- 2
13878 is composite. Its prime factorisation is
- 3
The divisors add up to 30960; without 13878 itself that is 17082, so 13878 is abundant (17082 is more than 13878). Euler's totient φ(13878) = 4608 numbers up to 13878 share no factor with it.
- 4
The digits of 13878 add up to 27, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 89 steps to reach 1.
LaTeX source of the formulas on this page
\[ 13878 = 2 \times 3^{3} \times 257 \]13878 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 16 |
| Sum of divisors | 30960 |
| Euler totient φ(n) | 4608 |
| Square | 192598884 |
| Cube | 2672887312152 |
| Square root | 117.804923 (= 3√1542) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 89 |
| Scientific notation | 1.3878 × |
13878 in other forms
| Form | Value |
|---|---|
| In words | thirteen thousand eight hundred and seventy-eight |
| Binary (base 2) | 11011000110110 |
| Octal (base 8) | 33066 |
| Hexadecimal (base 16) | 3636 |
| Base 3 | 201001000 |
| As time | 13878 seconds = 3 h 51 min 18 s |
Is 13878 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (13878 ÷ 2 = 6939) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (13878 ÷ 3 = 4626) | 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 (13878 ÷ 6 = 2313) | 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 | Yes (13878 ÷ 9 = 1542) | 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 7) | 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 13878 a prime number?
No. 13878 = 2 × × 257, so it is divisible by 2.
What are the factors of 13878?
1, 2, 3, 6, 9, 18, 27, 54, 257, 514, 771, 1542, 2313, 4626, 6939, 13878.
What is 13878 in binary?
11011000110110 (hexadecimal 3636, octal 33066).
What is the square root of 13878?
About 117.8049, exactly 3√1542.
Is 13878 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 13878?
13878 is a Harshad number: divisible by its digit sum 27.