The number 16384
16384 is a power of 2 () and a perfect square (128²). Its prime factorisation is . Divisors (15): 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 16384: a power of 2 (); a perfect square (128²).
- 2
16384 is composite. Its prime factorisation is
- 3
The divisors add up to 32767; without 16384 itself that is 16383, so 16384 is deficient (16383 is less than 16384). Euler's totient φ(16384) = 8192 numbers up to 16384 share no factor with it.
- 4
The digits of 16384 add up to 22, and repeating that until one digit is left gives the digital root 4. The Collatz sequence (halve if even, else 3n+1) takes 14 steps to reach 1.
LaTeX source of the formulas on this page
\[ 16384 = 2^{14} \]16384 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 15 |
| Sum of divisors | 32767 |
| Euler totient φ(n) | 8192 |
| Square | 268435456 |
| Cube | 4398046511104 |
| Square root | 128 |
| Digit sum / digital root | 22 / 4 |
| Collatz steps to 1 | 14 |
| Scientific notation | 1.6384 × |
| Perfect power |
16384 in other forms
| Form | Value |
|---|---|
| In words | sixteen thousand three hundred and eighty-four |
| Binary (base 2) | 100000000000000 |
| Octal (base 8) | 40000 |
| Hexadecimal (base 16) | 4000 |
| Base 3 | 211110211 |
| As time | 16384 seconds = 4 h 33 min 4 s |
Is 16384 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (16384 ÷ 2 = 8192) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 1) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (16384 ÷ 4 = 4096) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 4) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 4) | 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 | Yes (16384 ÷ 8 = 2048) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 4) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 4) | 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 4) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 16384 a prime number?
No. 16384 = , so it is divisible by 2.
What are the factors of 16384?
1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384.
What is 16384 in binary?
100000000000000 (hexadecimal 4000, octal 40000).
What is the square root of 16384?
128, because 128 × 128 = 16384.
Is 16384 divisible by 3?
No. Its digits add up to 22, which is not a multiple of 3.
What is special about the number 16384?
16384 is a power of 2 (); a perfect square (128²).