The number 34816
34816 is a composite number with 24 divisors. Its prime factorisation is × 17. Divisors (24): 1, 2, 4, 8, 16, 17, 32, 34, 64, 68, 128, 136, 256, 272, 512, 544 … 34816.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
34816 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
34816 is composite. Its prime factorisation is
- 3
The divisors add up to 73710; without 34816 itself that is 38894, so 34816 is abundant (38894 is more than 34816). Euler's totient φ(34816) = 16384 numbers up to 34816 share no factor with it.
- 4
The digits of 34816 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 23 steps to reach 1.
LaTeX source of the formulas on this page
\[ 34816 = 2^{11} \times 17 \]34816 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 73710 |
| Euler totient φ(n) | 16384 |
| Square | 1212153856 |
| Cube | 42202348650496 |
| Square root | 186.590461 (= 32√34) |
| Digit sum / digital root | 22 / 4 |
| Collatz steps to 1 | 23 |
| Scientific notation | 3.4816 × |
34816 in other forms
| Form | Value |
|---|---|
| In words | thirty-four thousand eight hundred and sixteen |
| Binary (base 2) | 1000100000000000 |
| Octal (base 8) | 104000 |
| Hexadecimal (base 16) | 8800 |
| Base 3 | 1202202111 |
| As time | 34816 seconds = 9 h 40 min 16 s |
Is 34816 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (34816 ÷ 2 = 17408) | 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 (34816 ÷ 4 = 8704) | 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 5) | 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 (34816 ÷ 8 = 4352) | 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 6) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 1) | 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 34816 a prime number?
No. 34816 = × 17, so it is divisible by 2.
What are the factors of 34816?
1, 2, 4, 8, 16, 17, 32, 34, 64, 68, 128, 136, 256, 272, 512, 544, 1024, 1088, 2048, 2176, 4352, 8704, 17408, 34816.
What is 34816 in binary?
1000100000000000 (hexadecimal 8800, octal 104000).
What is the square root of 34816?
About 186.5905, exactly 32√34.
Is 34816 divisible by 3?
No. Its digits add up to 22, which is not a multiple of 3.
What is special about the number 34816?
It is a composite number with 24 divisors.