The number 83984
83984 is a composite number with 20 divisors. Its prime factorisation is × 29 × 181. Divisors (20): 1, 2, 4, 8, 16, 29, 58, 116, 181, 232, 362, 464, 724, 1448, 2896, 5249 … 83984.
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How to work it out
- 1
83984 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
83984 is composite. Its prime factorisation is
- 3
The divisors add up to 169260; without 83984 itself that is 85276, so 83984 is abundant (85276 is more than 83984). Euler's totient φ(83984) = 40320 numbers up to 83984 share no factor with it.
- 4
The digits of 83984 add up to 32, and repeating that until one digit is left gives the digital root 5. The Collatz sequence (halve if even, else 3n+1) takes 133 steps to reach 1.
LaTeX source of the formulas on this page
\[ 83984 = 2^{4} \times 29 \times 181 \]83984 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 20 |
| Sum of divisors | 169260 |
| Euler totient φ(n) | 40320 |
| Square | 7053312256 |
| Cube | 592365376507904 |
| Square root | 289.799931 (= 4√5249) |
| Digit sum / digital root | 32 / 5 |
| Collatz steps to 1 | 133 |
| Scientific notation | 8.3984 × |
83984 in other forms
| Form | Value |
|---|---|
| In words | eighty-three thousand nine hundred and eighty-four |
| Binary (base 2) | 10100100000010000 |
| Octal (base 8) | 244020 |
| Hexadecimal (base 16) | 14810 |
| Base 3 | 11021012112 |
| As time | 83984 seconds = 23 h 19 min 44 s |
Is 83984 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (83984 ÷ 2 = 41992) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 2) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (83984 ÷ 4 = 20996) | 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 2) | 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 (83984 ÷ 8 = 10498) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 5) | 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 10) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 8) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 83984 a prime number?
No. 83984 = × 29 × 181, so it is divisible by 2.
What are the factors of 83984?
1, 2, 4, 8, 16, 29, 58, 116, 181, 232, 362, 464, 724, 1448, 2896, 5249, 10498, 20996, 41992, 83984.
What is 83984 in binary?
10100100000010000 (hexadecimal 14810, octal 244020).
What is the square root of 83984?
About 289.7999, exactly 4√5249.
Is 83984 divisible by 3?
No. Its digits add up to 32, which is not a multiple of 3.
What is special about the number 83984?
It is a composite number with 20 divisors.