The number 83904
83904 is a composite number with 56 divisors. Its prime factorisation is × 3 × 19 × 23. Divisors (56): 1, 2, 3, 4, 6, 8, 12, 16, 19, 23, 24, 32, 38, 46, 48, 57 … 83904.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 83904: a Harshad number: divisible by its digit sum 24.
- 2
83904 is composite. Its prime factorisation is
- 3
The divisors add up to 243840; without 83904 itself that is 159936, so 83904 is abundant (159936 is more than 83904). Euler's totient φ(83904) = 25344 numbers up to 83904 share no factor with it.
- 4
The digits of 83904 add up to 24, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 107 steps to reach 1.
LaTeX source of the formulas on this page
\[ 83904 = 2^{6} \times 3 \times 19 \times 23 \]83904 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 56 |
| Sum of divisors | 243840 |
| Euler totient φ(n) | 25344 |
| Square | 7039881216 |
| Cube | 590674193547264 |
| Square root | 289.661872 (= 8√1311) |
| Digit sum / digital root | 24 / 6 |
| Collatz steps to 1 | 107 |
| Scientific notation | 8.3904 × |
83904 in other forms
| Form | Value |
|---|---|
| In words | eighty-three thousand nine hundred and four |
| Binary (base 2) | 10100011111000000 |
| Octal (base 8) | 243700 |
| Hexadecimal (base 16) | 147C0 |
| Base 3 | 11021002120 |
| As time | 83904 seconds = 23 h 18 min 24 s |
Is 83904 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (83904 ÷ 2 = 41952) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (83904 ÷ 3 = 27968) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (83904 ÷ 4 = 20976) | 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 | Yes (83904 ÷ 6 = 13984) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 2) | 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 (83904 ÷ 8 = 10488) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 6) | 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 7) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (83904 ÷ 12 = 6992) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 83904 a prime number?
No. 83904 = × 3 × 19 × 23, so it is divisible by 2.
What are the factors of 83904?
1, 2, 3, 4, 6, 8, 12, 16, 19, 23, 24, 32, 38, 46, 48, 57, 64, 69, 76, 92, 96, 114, 138, 152, 184, 192, 228, 276, 304, 368, 437, 456, 552, 608, 736, 874, 912, 1104, 1216, 1311, 1472, 1748, 1824, 2208, 2622, 3496, 3648, 4416, 5244, 6992, 10488, 13984, 20976, 27968, 41952, 83904.
What is 83904 in binary?
10100011111000000 (hexadecimal 147C0, octal 243700).
What is the square root of 83904?
About 289.6619, exactly 8√1311.
Is 83904 divisible by 3?
Yes. Its digits add up to 24, a multiple of 3.
What is special about the number 83904?
83904 is a Harshad number: divisible by its digit sum 24.