The number 83808
83808 is a composite number with 48 divisors. Its prime factorisation is × × 97. Divisors (48): 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54 … 83808.
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How to work it out
- 1
What is special about 83808: a Harshad number: divisible by its digit sum 27.
- 2
83808 is composite. Its prime factorisation is
- 3
The divisors add up to 246960; without 83808 itself that is 163152, so 83808 is abundant (163152 is more than 83808). Euler's totient φ(83808) = 27648 numbers up to 83808 share no factor with it.
- 4
The digits of 83808 add up to 27, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 107 steps to reach 1.
LaTeX source of the formulas on this page
\[ 83808 = 2^{5} \times 3^{3} \times 97 \]83808 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 246960 |
| Euler totient φ(n) | 27648 |
| Square | 7023780864 |
| Cube | 588649026650112 |
| Square root | 289.496114 (= 12√582) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 107 |
| Scientific notation | 8.3808 × |
83808 in other forms
| Form | Value |
|---|---|
| In words | eighty-three thousand eight hundred and eight |
| Binary (base 2) | 10100011101100000 |
| Octal (base 8) | 243540 |
| Hexadecimal (base 16) | 14760 |
| Base 3 | 11020222000 |
| As time | 83808 seconds = 23 h 16 min 48 s |
Is 83808 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (83808 ÷ 2 = 41904) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (83808 ÷ 3 = 27936) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (83808 ÷ 4 = 20952) | 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 | Yes (83808 ÷ 6 = 13968) | 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 (83808 ÷ 8 = 10476) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (83808 ÷ 9 = 9312) | 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 10) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (83808 ÷ 12 = 6984) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 83808 a prime number?
No. 83808 = × × 97, so it is divisible by 2.
What are the factors of 83808?
1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 72, 96, 97, 108, 144, 194, 216, 288, 291, 388, 432, 582, 776, 864, 873, 1164, 1552, 1746, 2328, 2619, 3104, 3492, 4656, 5238, 6984, 9312, 10476, 13968, 20952, 27936, 41904, 83808.
What is 83808 in binary?
10100011101100000 (hexadecimal 14760, octal 243540).
What is the square root of 83808?
About 289.4961, exactly 12√582.
Is 83808 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 83808?
83808 is a Harshad number: divisible by its digit sum 27.