The number 16383
16383 is a binary palindrome (11111111111111). Its prime factorisation is 3 × 43 × 127. Divisors (8): 1, 3, 43, 127, 129, 381, 5461, 16383.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 16383: a binary palindrome (11111111111111).
- 2
16383 is composite. Its prime factorisation is
- 3
The divisors add up to 22528; without 16383 itself that is 6145, so 16383 is deficient (6145 is less than 16383). Euler's totient φ(16383) = 10584 numbers up to 16383 share no factor with it.
- 4
The digits of 16383 add up to 21, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 159 steps to reach 1.
LaTeX source of the formulas on this page
\[ 16383 = 3 \times 43 \times 127 \]
16383 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 8 |
| Sum of divisors | 22528 |
| Euler totient φ(n) | 10584 |
| Square | 268402689 |
| Cube | 4397241253887 |
| Square root | 127.996094 |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 159 |
| Scientific notation | 1.6383 × |
16383 in other forms
| Form | Value |
|---|---|
| In words | sixteen thousand three hundred and eighty-three |
| Binary (base 2) | 11111111111111 |
| Octal (base 8) | 37777 |
| Hexadecimal (base 16) | 3FFF |
| Base 3 | 211110210 |
| As time | 16383 seconds = 4 h 33 min 3 s |
Is 16383 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | No (remainder 1) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (16383 ÷ 3 = 5461) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 3) | 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 | No (remainder 3) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 3) | 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 7) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 3) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 3) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 4) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 3) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 16383 a prime number?
No. 16383 = 3 × 43 × 127, so it is divisible by 3.
What are the factors of 16383?
1, 3, 43, 127, 129, 381, 5461, 16383.
What is 16383 in binary?
11111111111111 (hexadecimal 3FFF, octal 37777).
What is the square root of 16383?
About 127.9961.
Is 16383 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 16383?
16383 is a binary palindrome (11111111111111).