The number 4096
4096 is a power of 2 () and a perfect square (64²). Its prime factorisation is . Divisors (13): 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 4096: a power of 2 (); a perfect square (64²); a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
4096 is composite. Its prime factorisation is
- 3
The divisors add up to 8191; without 4096 itself that is 4095, so 4096 is deficient (4095 is less than 4096). Euler's totient φ(4096) = 2048 numbers up to 4096 share no factor with it.
- 4
The digits of 4096 add up to 19, and repeating that until one digit is left gives the digital root 1. The Collatz sequence (halve if even, else 3n+1) takes 12 steps to reach 1.
LaTeX source of the formulas on this page
\[ 4096 = 2^{12} \]4096 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 13 |
| Sum of divisors | 8191 |
| Euler totient φ(n) | 2048 |
| Square | 16777216 |
| Cube | 68719476736 |
| Square root | 64 |
| Digit sum / digital root | 19 / 1 |
| Collatz steps to 1 | 12 |
| Scientific notation | 4.096 × |
| Perfect power |
4096 in other forms
| Form | Value |
|---|---|
| In words | four thousand and ninety-six |
| Binary (base 2) | 1000000000000 |
| Octal (base 8) | 10000 |
| Hexadecimal (base 16) | 1000 |
| Base 3 | 12121201 |
| As time | 4096 seconds = 1 h 8 min 16 s |
Is 4096 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (4096 ÷ 2 = 2048) | 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 (4096 ÷ 4 = 1024) | 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 4) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 1) | 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 (4096 ÷ 8 = 512) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 1) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 6) | 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 4) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 4096 a prime number?
No. 4096 = , so it is divisible by 2.
What are the factors of 4096?
1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096.
What is 4096 in binary?
1000000000000 (hexadecimal 1000, octal 10000).
What is the square root of 4096?
64, because 64 × 64 = 4096.
Is 4096 divisible by 3?
No. Its digits add up to 19, which is not a multiple of 3.
What is special about the number 4096?
4096 is a power of 2 (); a perfect square (64²); a happy number: repeatedly adding the squares of its digits reaches 1.