The number 32688
32688 is a composite number with 30 divisors. Its prime factorisation is × × 227. Divisors (30): 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144, 227 … 32688.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
32688 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
32688 is composite. Its prime factorisation is
- 3
The divisors add up to 91884; without 32688 itself that is 59196, so 32688 is abundant (59196 is more than 32688). Euler's totient φ(32688) = 10848 numbers up to 32688 share no factor with it.
- 4
The digits of 32688 add up to 27, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 160 steps to reach 1.
LaTeX source of the formulas on this page
\[ 32688 = 2^{4} \times 3^{2} \times 227 \]32688 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 30 |
| Sum of divisors | 91884 |
| Euler totient φ(n) | 10848 |
| Square | 1068505344 |
| Cube | 34927302684672 |
| Square root | 180.798230 (= 12√227) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 160 |
| Scientific notation | 3.2688 × |
32688 in other forms
| Form | Value |
|---|---|
| In words | thirty-two thousand six hundred and eighty-eight |
| Binary (base 2) | 111111110110000 |
| Octal (base 8) | 77660 |
| Hexadecimal (base 16) | 7FB0 |
| Base 3 | 1122211200 |
| As time | 32688 seconds = 9 h 4 min 48 s |
Is 32688 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (32688 ÷ 2 = 16344) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (32688 ÷ 3 = 10896) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (32688 ÷ 4 = 8172) | 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 | Yes (32688 ÷ 6 = 5448) | 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 (32688 ÷ 8 = 4086) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (32688 ÷ 9 = 3632) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 8) | 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 (32688 ÷ 12 = 2724) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 32688 a prime number?
No. 32688 = × × 227, so it is divisible by 2.
What are the factors of 32688?
1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144, 227, 454, 681, 908, 1362, 1816, 2043, 2724, 3632, 4086, 5448, 8172, 10896, 16344, 32688.
What is 32688 in binary?
111111110110000 (hexadecimal 7FB0, octal 77660).
What is the square root of 32688?
About 180.7982, exactly 12√227.
Is 32688 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 32688?
It is a composite number with 30 divisors.