The number 83184
83184 is a composite number with 20 divisors. Its prime factorisation is × 3 × 1733. Divisors (20): 1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 1733, 3466, 5199, 6932, 10398, 13864 … 83184.
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How to work it out
- 1
What is special about 83184: a Harshad number: divisible by its digit sum 24.
- 2
83184 is composite. Its prime factorisation is
- 3
The divisors add up to 215016; without 83184 itself that is 131832, so 83184 is abundant (131832 is more than 83184). Euler's totient φ(83184) = 27712 numbers up to 83184 share no factor with it.
- 4
The digits of 83184 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 151 steps to reach 1.
LaTeX source of the formulas on this page
\[ 83184 = 2^{4} \times 3 \times 1733 \]83184 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 20 |
| Sum of divisors | 215016 |
| Euler totient φ(n) | 27712 |
| Square | 6919577856 |
| Cube | 575598164373504 |
| Square root | 288.416366 (= 4√5199) |
| Digit sum / digital root | 24 / 6 |
| Collatz steps to 1 | 151 |
| Scientific notation | 8.3184 × |
83184 in other forms
| Form | Value |
|---|---|
| In words | eighty-three thousand one hundred and eighty-four |
| Binary (base 2) | 10100010011110000 |
| Octal (base 8) | 242360 |
| Hexadecimal (base 16) | 144F0 |
| Base 3 | 11020002220 |
| As time | 83184 seconds = 23 h 6 min 24 s |
Is 83184 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (83184 ÷ 2 = 41592) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (83184 ÷ 3 = 27728) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (83184 ÷ 4 = 20796) | 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 (83184 ÷ 6 = 13864) | 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 (83184 ÷ 8 = 10398) | 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 2) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (83184 ÷ 12 = 6932) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 83184 a prime number?
No. 83184 = × 3 × 1733, so it is divisible by 2.
What are the factors of 83184?
1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 1733, 3466, 5199, 6932, 10398, 13864, 20796, 27728, 41592, 83184.
What is 83184 in binary?
10100010011110000 (hexadecimal 144F0, octal 242360).
What is the square root of 83184?
About 288.4164, exactly 4√5199.
Is 83184 divisible by 3?
Yes. Its digits add up to 24, a multiple of 3.
What is special about the number 83184?
83184 is a Harshad number: divisible by its digit sum 24.