The number 83824
83824 is a composite number with 30 divisors. Its prime factorisation is × × 31. Divisors (30): 1, 2, 4, 8, 13, 16, 26, 31, 52, 62, 104, 124, 169, 208, 248, 338 … 83824.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
83824 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
83824 is composite. Its prime factorisation is
- 3
The divisors add up to 181536; without 83824 itself that is 97712, so 83824 is abundant (97712 is more than 83824). Euler's totient φ(83824) = 37440 numbers up to 83824 share no factor with it.
- 4
The digits of 83824 add up to 25, and repeating that until one digit is left gives the digital root 7. The Collatz sequence (halve if even, else 3n+1) takes 107 steps to reach 1.
LaTeX source of the formulas on this page
\[ 83824 = 2^{4} \times 13^{2} \times 31 \]83824 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 30 |
| Sum of divisors | 181536 |
| Euler totient φ(n) | 37440 |
| Square | 7026462976 |
| Cube | 588986232500224 |
| Square root | 289.523747 (= 52√31) |
| Digit sum / digital root | 25 / 7 |
| Collatz steps to 1 | 107 |
| Scientific notation | 8.3824 × |
83824 in other forms
| Form | Value |
|---|---|
| In words | eighty-three thousand eight hundred and twenty-four |
| Binary (base 2) | 10100011101110000 |
| Octal (base 8) | 243560 |
| Hexadecimal (base 16) | 14770 |
| Base 3 | 11020222121 |
| As time | 83824 seconds = 23 h 17 min 4 s |
Is 83824 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (83824 ÷ 2 = 41912) | 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 (83824 ÷ 4 = 20956) | 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 6) | 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 (83824 ÷ 8 = 10478) | 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 4) | 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 83824 a prime number?
No. 83824 = × × 31, so it is divisible by 2.
What are the factors of 83824?
1, 2, 4, 8, 13, 16, 26, 31, 52, 62, 104, 124, 169, 208, 248, 338, 403, 496, 676, 806, 1352, 1612, 2704, 3224, 5239, 6448, 10478, 20956, 41912, 83824.
What is 83824 in binary?
10100011101110000 (hexadecimal 14770, octal 243560).
What is the square root of 83824?
About 289.5237, exactly 52√31.
Is 83824 divisible by 3?
No. Its digits add up to 25, which is not a multiple of 3.
What is special about the number 83824?
It is a composite number with 30 divisors.