The number 16191
16191 is a binary palindrome (11111100111111). Its prime factorisation is × 7 × 257. Divisors (12): 1, 3, 7, 9, 21, 63, 257, 771, 1799, 2313, 5397, 16191.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 16191: a binary palindrome (11111100111111).
- 2
16191 is composite. Its prime factorisation is
- 3
The divisors add up to 26832; without 16191 itself that is 10641, so 16191 is deficient (10641 is less than 16191). Euler's totient φ(16191) = 9216 numbers up to 16191 share no factor with it.
- 4
The digits of 16191 add up to 18, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 115 steps to reach 1.
LaTeX source of the formulas on this page
\[ 16191 = 3^{2} \times 7 \times 257 \]16191 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 26832 |
| Euler totient φ(n) | 9216 |
| Square | 262148481 |
| Cube | 4244446055871 |
| Square root | 127.243860 (= 3√1799) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 115 |
| Scientific notation | 1.6191 × |
16191 in other forms
| Form | Value |
|---|---|
| In words | sixteen thousand one hundred and ninety-one |
| Binary (base 2) | 11111100111111 |
| Octal (base 8) | 37477 |
| Hexadecimal (base 16) | 3F3F |
| Base 3 | 211012200 |
| As time | 16191 seconds = 4 h 29 min 51 s |
Is 16191 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 (16191 ÷ 3 = 5397) | 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 1) | 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 | Yes (16191 ÷ 7 = 2313) | 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 | Yes (16191 ÷ 9 = 1799) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 1) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 10) | 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 16191 a prime number?
No. 16191 = × 7 × 257, so it is divisible by 3.
What are the factors of 16191?
1, 3, 7, 9, 21, 63, 257, 771, 1799, 2313, 5397, 16191.
What is 16191 in binary?
11111100111111 (hexadecimal 3F3F, octal 37477).
What is the square root of 16191?
About 127.2439, exactly 3√1799.
Is 16191 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 16191?
16191 is a binary palindrome (11111100111111).