The number 83968
83968 is a composite number with 24 divisors. Its prime factorisation is × 41. Divisors (24): 1, 2, 4, 8, 16, 32, 41, 64, 82, 128, 164, 256, 328, 512, 656, 1024 … 83968.
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How to work it out
- 1
83968 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
83968 is composite. Its prime factorisation is
- 3
The divisors add up to 171990; without 83968 itself that is 88022, so 83968 is abundant (88022 is more than 83968). Euler's totient φ(83968) = 40960 numbers up to 83968 share no factor with it.
- 4
The digits of 83968 add up to 34, and repeating that until one digit is left gives the digital root 7. The Collatz sequence (halve if even, else 3n+1) takes 120 steps to reach 1.
LaTeX source of the formulas on this page
\[ 83968 = 2^{11} \times 41 \]83968 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 171990 |
| Euler totient φ(n) | 40960 |
| Square | 7050625024 |
| Cube | 592026882015232 |
| Square root | 289.772324 (= 32√82) |
| Digit sum / digital root | 34 / 7 |
| Collatz steps to 1 | 120 |
| Scientific notation | 8.3968 × |
83968 in other forms
| Form | Value |
|---|---|
| In words | eighty-three thousand nine hundred and sixty-eight |
| Binary (base 2) | 10100100000000000 |
| Octal (base 8) | 244000 |
| Hexadecimal (base 16) | 14800 |
| Base 3 | 11021011221 |
| As time | 83968 seconds = 23 h 19 min 28 s |
Is 83968 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (83968 ÷ 2 = 41984) | 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 (83968 ÷ 4 = 20992) | 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 4) | 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 | Yes (83968 ÷ 8 = 10496) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 7) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 8) | 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 83968 a prime number?
No. 83968 = × 41, so it is divisible by 2.
What are the factors of 83968?
1, 2, 4, 8, 16, 32, 41, 64, 82, 128, 164, 256, 328, 512, 656, 1024, 1312, 2048, 2624, 5248, 10496, 20992, 41984, 83968.
What is 83968 in binary?
10100100000000000 (hexadecimal 14800, octal 244000).
What is the square root of 83968?
About 289.7723, exactly 32√82.
Is 83968 divisible by 3?
No. Its digits add up to 34, which is not a multiple of 3.
What is special about the number 83968?
It is a composite number with 24 divisors.