The number 83232
83232 is a composite number with 54 divisors. Its prime factorisation is × × . Divisors (54): 1, 2, 3, 4, 6, 8, 9, 12, 16, 17, 18, 24, 32, 34, 36, 48 … 83232.
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How to work it out
- 1
What is special about 83232: a Harshad number: divisible by its digit sum 18.
- 2
83232 is composite. Its prime factorisation is
- 3
The divisors add up to 251433; without 83232 itself that is 168201, so 83232 is abundant (168201 is more than 83232). Euler's totient φ(83232) = 26112 numbers up to 83232 share no factor with it.
- 4
The digits of 83232 add up to 18, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 182 steps to reach 1.
LaTeX source of the formulas on this page
\[ 83232 = 2^{5} \times 3^{2} \times 17^{2} \]83232 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 54 |
| Sum of divisors | 251433 |
| Euler totient φ(n) | 26112 |
| Square | 6927565824 |
| Cube | 576595158663168 |
| Square root | 288.499567 (= 204√2) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 182 |
| Scientific notation | 8.3232 × |
83232 in other forms
| Form | Value |
|---|---|
| In words | eighty-three thousand two hundred and thirty-two |
| Binary (base 2) | 10100010100100000 |
| Octal (base 8) | 242440 |
| Hexadecimal (base 16) | 14520 |
| Base 3 | 11020011200 |
| As time | 83232 seconds = 23 h 7 min 12 s |
Is 83232 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (83232 ÷ 2 = 41616) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (83232 ÷ 3 = 27744) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (83232 ÷ 4 = 20808) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 2) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (83232 ÷ 6 = 13872) | 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 (83232 ÷ 8 = 10404) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (83232 ÷ 9 = 9248) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 2) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 6) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (83232 ÷ 12 = 6936) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 83232 a prime number?
No. 83232 = × × , so it is divisible by 2.
What are the factors of 83232?
1, 2, 3, 4, 6, 8, 9, 12, 16, 17, 18, 24, 32, 34, 36, 48, 51, 68, 72, 96, 102, 136, 144, 153, 204, 272, 288, 289, 306, 408, 544, 578, 612, 816, 867, 1156, 1224, 1632, 1734, 2312, 2448, 2601, 3468, 4624, 4896, 5202, 6936, 9248, 10404, 13872, 20808, 27744, 41616, 83232.
What is 83232 in binary?
10100010100100000 (hexadecimal 14520, octal 242440).
What is the square root of 83232?
About 288.4996, exactly 204√2.
Is 83232 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 83232?
83232 is a Harshad number: divisible by its digit sum 18.