The number 32193
32193 is a composite number with 18 divisors. Its prime factorisation is × × 73. Divisors (18): 1, 3, 7, 9, 21, 49, 63, 73, 147, 219, 441, 511, 657, 1533, 3577, 4599 … 32193.
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How to work it out
- 1
32193 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
32193 is composite. Its prime factorisation is
- 3
The divisors add up to 54834; without 32193 itself that is 22641, so 32193 is deficient (22641 is less than 32193). Euler's totient φ(32193) = 18144 numbers up to 32193 share no factor with it.
- 4
The digits of 32193 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 46 steps to reach 1.
LaTeX source of the formulas on this page
\[ 32193 = 3^{2} \times 7^{2} \times 73 \]32193 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 18 |
| Sum of divisors | 54834 |
| Euler totient φ(n) | 18144 |
| Square | 1036389249 |
| Cube | 33364479093057 |
| Square root | 179.424079 (= 21√73) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 46 |
| Scientific notation | 3.2193 × |
32193 in other forms
| Form | Value |
|---|---|
| In words | thirty-two thousand one hundred and ninety-three |
| Binary (base 2) | 111110111000001 |
| Octal (base 8) | 76701 |
| Hexadecimal (base 16) | 7DC1 |
| Base 3 | 1122011100 |
| As time | 32193 seconds = 8 h 56 min 33 s |
Is 32193 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | No (remainder 1) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (32193 ÷ 3 = 10731) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 1) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 3) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 3) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (32193 ÷ 7 = 4599) | 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 | No (remainder 1) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (32193 ÷ 9 = 3577) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 3) | 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 | No (remainder 9) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 32193 a prime number?
No. 32193 = × × 73, so it is divisible by 3.
What are the factors of 32193?
1, 3, 7, 9, 21, 49, 63, 73, 147, 219, 441, 511, 657, 1533, 3577, 4599, 10731, 32193.
What is 32193 in binary?
111110111000001 (hexadecimal 7DC1, octal 76701).
What is the square root of 32193?
About 179.4241, exactly 21√73.
Is 32193 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 32193?
It is a composite number with 18 divisors.